Physical factors governing AEC vary significantly with altitude. Local emissions and chemical composition dominate near-surface AEC (Xiong et al., 2026; Jiang et al., 2024), whereas long-range transport and regional backgrounds dictate the free troposphere (Uno et al., 2009; Val Martin et al., 2013). To reflect this stratification, we design a gated feature fusion mechanism within the VPS. Instead of statically concatenating inputs, this module dynamically weights the contributions of physicochemical profiles, height information, and spatiotemporal indices for each altitude layer. This allows the model to autonomously prioritize the most relevant physical drivers at specific heights.

The SFS incorporates diverse meteorological parameters with distinct physical units. To prevent the network from treating these distinct physical quantities merely as dimensionless numbers, we implement a variable identity embedding (Eq. S4 in the Supplement). This mechanism assigns a unique physical tag to each 2D variable, ensuring the model accurately distinguishes between different meteorological forcing factors when modulating the AEC simulation bias.

Aerosol layers are inherently coupled through vertical exchange processes such as turbulent mixing, deep convection, and gravitational sedimentation. We employ a Transformer encoder stack to explicitly model this vertical connectivity. Its self-attention mechanism acts as a dynamic vertical covariance operator (detailed in Sect. S4c). It facilitates information flow between near-surface accumulation layers and high-altitude transport layers, ensuring the rectified AEC profile maintains physical continuity.

To constrain this vertical AEC bias correction with synoptic meteorology, we introduce a cross-attention layer. Functionally, this mechanism acts as a dynamic diagnostic process. It allows the aerosol state at each specific altitude to dynamically respond to the prevailing synoptic conditions (e.g., surface wind speed, PBLH), thereby extracting relevant environmental constraints for the local bias adjustment. This design mimics physical reality, where synoptic meteorological backgrounds continuously modulate local microphysical structures.

To predict the final AEC bias, we employ a residual connection that adds the initial baseline state (from the VPS) directly to the output of the cross-attention module (which has already fused the encoded VPS with the SFS). Physically, this residual design serves as a critical prior constraint. It anchors the network to the fundamental atmospheric state provided by GEOS-Chem, ensuring the model computes a meteorology-driven perturbation rather than generating unphysical aerosol signals. Subsequently, the integrated features undergo a progressive dimension-reduction (represented as D→D/2→D/4 in Fig. 2). This architecture functions as an information funnel, filtering redundant meteorological noise and distilling the non-linear interactions among diverse drivers to accurately quantify the true magnitude of the AEC biases.

We employ distinct attribution methods tailored to the hybrid inputs to capture micro-scale responses. For the VPS, we apply gradient-based attribution, utilizing the Input × Gradient method (Shrikumar et al., 2017) to quantify the sensitivity of AEC bias correction to physicochemical profiles. Simultaneously, Cross-Attention weights are extracted to map the interaction strength between the SFS and the VPS, revealing how synoptic forcing modulates vertical profile rectifications. Furthermore, to understand the model's internal decision-making, we analyze the learnable weights of the gated feature fusion mechanism (detailed in Sect. 3.2.1). This analysis visualizes the altitude-dependent prioritization among the four VPS components: physicochemical profiles, height information, spatial coordinates, and temporal indices.

To assess the model's reliance on the overarching input feature groups (the VPS and SFS), we perform permutation feature importance analysis (detailed in Sect. S7d). By measuring the percentage increase in Mean Squared Error (MSE) when specific groups are randomly shuffled, this method provides a domain-wide approach to identify the fundamental predictors essential for AEC bias correction.

Considering the spatial heterogeneity of aerosol sources, SHAP Analysis is used to dissect regional dependencies and feature interactions. We employ a K-means clustering strategy to construct a representative background dataset capturing diverse atmospheric states (detailed in Sect. S8). SHAP values are computed for the designated ROI to reveal how dominant AEC bias drivers shift under different environmental regimes.

To quantitatively assess the model's robustness in capturing the non-linear mapping between GEOS-Chem simulation biases and atmospheric states, we execute a LOYO cross-validation strategy comprising three independent experiments (Table 1). The Transformer achieves a high average R of 0.659 and a low MAE of 0.014 km⁻¹ on the independent test years (Table 2). These metrics demonstrate robust predictive skill, confirming that the model has successfully learned to reproduce the systematic component of extinction biases from the input state variables. Notably, a comparison with the internal validation results (Table S2) reveals that the model's performance on the unseen test sets is comparable to – and in some metrics marginally superior to – that on the validation sets. This consistency suggests that the Transformer architecture has extracted time-invariant, physically meaningful representations of aerosol bias mechanisms rather than overfitting to specific temporal anomalies in the training data. The ability to generalize to years with distinct meteorological interactions underscores the model's potential for operational bias correction.

We further examine the temporal stability of the model by analyzing monthly variations in the predictive accuracy of the AEC simulation bias (Fig. 3). The model exhibits a distinct seasonal pattern characterized by superior performance in winter and a moderate decline in summer. During the winter months (December–February), R consistently peaks above 0.7. This enhanced performance is attributed to the synergistic effect of favorable meteorology and observational quality. Specifically, the lower solar elevation angle in winter minimizes solar background noise, thereby enhancing the Signal-to-Noise Ratio (SNR) of the CALIOP retrievals compared to the strong background illumination present in summer (Zhen et al., 2024). Additionally, the stable boundary layer in winter confines aerosols to lower altitudes (Xiong et al., 2026), creating sharper vertical gradients that are physically more distinct for the network to capture. In contrast, a discernible decline in performance occurs during the summer (June–August) over EA. This reduction implies a compound mechanism driven by both data scarcity and observational uncertainty. First, the decline coincides with a sharp decrease in the effective sample size (Fig. 3a, gray bars). This is mechanically linked to the Asian Summer Monsoon, where frequent cloud cover necessitates the exclusion of a significant volume of cloud-contaminated CALIOP profiles (Winker et al., 2009, 2013; Vernier et al., 2011), thereby reducing the representativeness of training data for complex convective scenarios. Second, and more critically, the inherently lower SNR in summer observations imposes a theoretical ceiling on point-to-point correlation metrics. Since random noise in the validation target (CALIOP) cannot be physically predicted, it naturally degrades the R, even if the model correctly retrieves the underlying aerosol signal.

Crucially, despite the fluctuations in linear correlation driven by these external sampling and observational constraints, the model demonstrates remarkable stability in correcting systematic biases. Figure 3c illustrates that the monthly mean bias remains tightly constrained within ±0.01 km⁻¹ throughout the year, exhibiting negligible seasonal drift even during the challenging summer months. This decoupling of metrics implies that while random noise (reflected in lower R) increases in summer due to complex meteorology and reduced SNR, the model does not introduce systematic artifacts. This conclusion is further supported by internal validation results (Fig. S2), which confirm that performance fluctuations are a response to data quality rather than intrinsic model instability. Moreover, detailed monthly density scatter plots (Figs. S3–S5) visually corroborate this robustness, revealing that the majority of predictions remain tightly clustered around the 1:1 identity line, independent of the season.

Given the critical importance of vertical stratification in radiative forcing calculations, we further scrutinize the model's performance as a function of altitude. A distinct advantage of this study, unlike traditional bias correction methods limited to column-integrated parameters, lies in its capability to finely resolve vertical aerosol structures. As evidenced by the vertical profiles of evaluation metrics (Fig. 4a), the model achieves peak performance within the bulk of the PBL (0.5–1.5 km), where R consistently exceeds 0.7. This altitude range corresponds to the region with the heaviest aerosol loading and the most complex chemical composition (Xiong et al., 2026; Jiang et al., 2024). This superior skill suggests that the Transformer's self-attention mechanism effectively captures the steep vertical gradients and pollutant accumulation patterns driven by boundary layer dynamics. Furthermore, the NRMSE (Fig. 4b) remains suppressed below 5 % throughout the entire 0–6 km column. This low error magnitude indicates that the model maintains consistent relative predictive accuracy even in the cleaner free troposphere, avoiding the generation of spurious artifacts often seen in DL applications on sparse data. Finally, the vertical profile of mean bias (Fig. 4c) fluctuates narrowly around zero at all altitude levels. This confirms the model's low systematic bias in the vertical dimension, ensuring that the correction process mitigates existing simulation errors without introducing new artificial biases.

Beyond capturing vertical structures, the capacity to resolve the spatial heterogeneity of systematic biases is vital for correcting 3D aerosol fields. In the primary study domain (EA), the Transformer demonstrates high precision in reproducing the complex spatial bias modes of the original GEOS-Chem simulation (Fig. 5, columns 1–3). Specifically, the model accurately captures the systematic underestimation over major anthropogenic and biomass burning source regions, including the NCP, IGP, and Indochina Peninsula. Over regions like the IGP, this negative simulation bias is primarily driven by the underrepresentation of local biofuel and agricultural emissions in traditional inventories (McDuffie et al., 2020), coupled with simplified aerosol mixing state assumptions that underestimate extinction enhancement under high humidity (Burgos et al., 2020; Zhai et al., 2021). Furthermore, the model's excessive numerical diffusion, a common limitation in CTMs, artificially dilutes the strong near-surface pollutant accumulation bounded by local topography (e.g., the Himalayas) (Eastham and Jacob, 2017). The GC-TF framework effectively identifies and mitigates these state-dependent underestimations. Additionally, it rectifies the biases over natural dust sources like the Taklamakan Desert. Conversely, it correctly identifies regions of systematic overestimation, predominantly located over the remote Western Pacific Ocean, the high-altitude Tibetan Plateau, and high-latitude terrestrial regions (e.g., Siberia). These capabilities suggest that the model effectively differentiates between bias regimes associated with distinct environments: it mitigates the systematic overestimation in clean background regions while concurrently compensating for the underestimation of source intensities in high-loading regions.

However, a localized area of strong positive AEC simulation bias (GEOS-Chem overestimation) appears in Central China in the 2019 target map (Fig. 5c), which is not fully reproduced by the prediction (Fig. 5g). We attribute this discrepancy primarily to observational sparsity and the episodic nature of the bias. Specifically, this region corresponds to a significantly lower density of valid CALIOP samples compared to the surrounding domain (Fig. S6), likely resulting from retrieval limitations associated with complex terrain and frequent cloud cover. Furthermore, monthly decomposition reveals that this elevated annual mean AEC simulation bias is predominantly driven by extreme values in January (Fig. S7), representing a transient winter episode specific to the 2019 test year. In such data-sparse regimes, the physics-informed Transformer model yields conservative predictions, suggesting that it prioritizes learning generalized physical laws over overfitting to localized outliers or specific interannual anomalies under-represented in the training distribution.

Crucially, the fourth column of Fig. 5 (2018 NA) presents a rigorous “out-of-domain” generalization test, where the model trained exclusively on EA data is directly applied to NA. Despite distinct differences in emission inventories and meteorological backgrounds between the two continents, the model exhibits remarkable spatial transferability. It successfully predicts the systematic underestimation over the Eastern United States and the overestimation over coastal areas (e.g., the Gulf of Mexico and the Atlantic coast), mirroring the actual GEOS-Chem AEC bias patterns (Target). This successful spatial extrapolation strongly suggests that the physics-informed Transformer model has learned the universal physical mapping between comprehensive atmospheric state variables (detailed in Table S1) and CTM simulation biases, rather than merely overfitting to the geographical coordinates or specific emission patterns of the EA training domain.

As discussed in Sect. 3.1, using satellite retrievals as the learning target inherently absorbs CALIOP's systematic uncertainties. To quantify how this observational limitation impacts the reliability of our framework, we conduct a perturbation-based sensitivity analysis (detailed in Sect. S13). We retrain the GC-TF model by artificially injecting a ±5 % systematic perturbation into the CALIOP AEC learning target.

Table S3 and Fig. S17 demonstrate that this systematic perturbation induces only a narrow envelope of variation in the corrected AEC profiles. The absolute shift in the mean bias fluctuates tightly between 0.001 and 0.004 km⁻¹, and the perturbed predictive RMSE (0.040 km⁻¹) consistently outperforms the original GEOS-Chem simulation (0.052 km⁻¹) by a large margin. This confirms that while observational uncertainties theoretically bound the absolute precision, the physics-informed Transformer does not uncontrollably amplify these errors, ensuring the robustness of the data-driven correction.

To justify the architectural complexity and isolate the sources of performance gains, we conduct comprehensive benchmarking and ablation studies using the independent 2017 test dataset (Table S5). When trained with identical GEOS-Chem and MERRA-2 predictors, the proposed Transformer significantly outperforms conventional machine learning baselines. A standard Multilayer Perceptron (MLP) and a 1-Dimensional Convolutional Neural Network (1D-CNN) yielded substantially lower R (R=0.083 and 0.540, respectively) compared to the Transformer (R=0.666). This performance gap confirms that global sequence modeling via self-attention is critical for capturing the long-range vertical coupling of atmospheric aerosols – such as boundary layer-to-free troposphere exchange – which localized convolutions or point-wise networks fail to resolve.

Furthermore, ablation experiments confirm that the performance enhancements are intrinsically linked to our structural designs. Removing the Gated Feature Fusion or the Cross-Attention module noticeably degrades predictive accuracy (Table S5). More importantly, beyond statistical improvements, these modules are physically indispensable. They transition the framework from a black-box predictor into a diagnostic tool, providing the explicit attention weights necessary to quantify height-dependent physical drivers (Sect. 4.5.1) and surface environmental modulations (Sect. 4.5.3).

To quantify the efficacy of the GEOS-Chem corrected by Transformer (GC-TF) model in correcting the magnitude of the AEC, we first compare the overall statistical relationship between simulated values and CALIOP observations across three independent test years from 2017 to 2019 (Fig. 6). The original GEOS-Chem simulation AEC exhibits a dispersed distribution around the 1:1 identity line, with R ranging only from 0.50 to 0.53 and RMSE remaining high at 0.052–0.055 km⁻¹. Notably, the low linear regression slopes (0.46–0.51) of the original simulation indicate a tendency to underestimate aerosol extinction intensity under high-loading conditions. In contrast, after correction by the GC-TF model, the AEC data points converge significantly toward the 1:1 line. The R for AEC improves to 0.66–0.73, the RMSE decreases by approximately 25 % (to 0.039–0.042 km⁻¹), and the regression slope recovers to 0.55–0.60. These results demonstrate that the framework effectively reduces random biases and realigns the dynamic range of simulated extinction with observations.

Despite these substantial statistical improvements, visual scatter remains in the density plots. To rigorously quantify these discrepancies, an error envelope of ± 0.15 km⁻¹ is introduced in Fig. 6d–f. Statistical analysis indicates that outliers exceeding this threshold account for only 1.20 % of the total dataset. Further diagnostic analysis (detailed in Sect. S10) reveals that these extreme deviations are not random noise but exhibit distinct spatial clustering over major emission hotspots (e.g., the IGP, the NCP, and the Indochina Peninsula), and are vertically confined within the PBL (<1.5 km a.g.l.). These residuals are primarily driven by representativeness errors: CALIOP's narrow footprint captures transient, highly concentrated sub-grid aerosol plumes, which are inherently smoothed out during the spatial averaging process across the coarse 2° × 2.5° grid of GEOS-Chem. Consequently, the GC-TF model captures the systematic, state-dependent biases of the grid mean, rather than fitting stochastic sub-grid extremes.

It is acknowledged that the high proportion of clean background samples (e.g., in the upper troposphere) contributes to the overall correlation metrics. To rigorously assess the model's capability in capturing effective aerosol signals – rather than merely fitting the zero-value baseline – we conduct a threshold-based sensitivity analysis (Fig. S9). As the extinction threshold increases from 0.00 to 0.20 km⁻¹, effectively filtering out background noise and isolating optically thick aerosol layers, the GC-TF model consistently outperforms the original GEOS-Chem simulation across all three independent test years. Although the R values naturally decline as the sample size shrinks to focus exclusively on extreme pollution events (indicated by the declining gray dashed line in Fig. S9), the corrected results maintain a persistent performance advantage over the original simulation. This confirms that the framework effectively rectifies structural biases in high-AEC regimes and that its performance gains are not merely artifacts of correctly predicting clean background states.

Further analysis of the vertical structure reveals more complex characteristics of the model AEC bias. The annual mean vertical extinction profiles for the three test years (Fig. 7) reveal a phenomenon: although the low slope in the scatter plots implies an “underestimation” of strong signals, the annual mean profiles reveal that the original GEOS-Chem exhibits a systematic “overestimation” relative to CALIOP observations within the boundary layer (<2 km). This apparent contradiction between macroscopic statistical metrics and the vertical mean state actually exposes the typical “excessive diffusion” issue in CTM simulations: the model struggles to capture the peaks of extreme pollution events (leading to regression slopes < 1) while systematically overestimating widespread background aerosol concentrations (resulting in higher intercepts and a systematic overestimation of the mean profile). The GC-TF model successfully addresses this by performing a bidirectional correction: mitigating the systemic overestimation in background regions while recovering the high-loading signals attenuated by model diffusion. In particular, the corrected results neither introduce spurious artifacts nor result in over-smoothing, accurately preserving vertical variation trends consistent with observations even in the free troposphere where aerosol loading is low.

It is important to note that while the absolute magnitude of the residual error (i.e., the remaining bias of the corrected AEC relative to observations) remains highest in the near-surface layer (0–1 km) due to the significantly higher aerosol base loading in the PBL (Fig. 7), the GC-TF model demonstrates its most critical contribution in this 0–1 km layer. It effectively bridges the gap between original simulations and observations, reducing the mean AEC simulation bias by 33 %–95 % across the independent test years (Fig. 7). Seasonal analysis (Fig. S10) further confirms that the model robustly reduces simulation biases in the near-surface layer, regardless of the season. This substantial reduction in near-surface bias is particularly vital for accurately deriving surface PM_2.5 concentrations and assessing aerosol health impacts.

The model's capacity to capture spatial heterogeneity is further validated through regional analysis (Figs. S11–S13) and explicit vertical bias profiles (Fig. S14). Rather than merely learning a globally uniform bias factor, the GC-TF model exhibits significant state-dependent adaptability. In the anthropogenic-dominated NCP and IGP, as well as the dust-dominated Taklamakan Desert, where the original model shows significant underestimation (Figs. S11–S13a, b, c), the GC-TF model successfully enhances the AEC to match observations, effectively pulling the negative bias profiles back toward the zero-reference line (Fig. S14a–c). Additionally, in the Indochina Peninsula, GEOS-Chem exhibits a spurious extinction peak near 0.8 km (Fig. S11d) likely due to mischaracterized injection heights of biomass burning smoke. The GC-TF model significantly attenuates this spurious peak. Conversely, over the relatively clean Western Pacific, the model effectively reduces simulated values to address overestimation (Fig. S11f). This ability to adaptively adjust the correction direction – enhancing in polluted regions while suppressing in clean marine environments – confirms the model's sensitivity to diverse underlying surfaces and emission regimes.

To further evaluate the model's precision in resolving the macroscopic spatial-vertical structure of AEC, we analyze the zonal mean vertical distribution of AEC over EA (70–150° E) for the 2019 test year (Fig. 8). CALIOP observations (Fig. 8a) identify a prominent aerosol high-loading belt concentrated between 20 and 30° N, corresponding to major anthropogenic sources in South and East Asia. This aerosol layer is predominantly confined to the lower troposphere below 2 km, with a high-extinction core concentrated within the lowest 1 km. In contrast, the original GEOS-Chem simulation (Fig. 8b) exhibits a characteristic “excessive diffusion” bias: the high-extinction layer is vertically over-extended (reaching above 3 km) and meridionally spread into the clean tropical regions south of 10° N, resulting in a southward displacement of the pollution center. The GC-TF model successfully rectifies these biases by re-centering the high-concentration core to the observed 25° N latitude and effectively constraining the vertical extent of the aerosol layer. By constraining the vertical extent of aerosols, the model reduces the spurious diffusion into the free troposphere and restores the peak extinction intensity suppressed by model smoothing.

Figure 9 further illustrates the annual mean longitudinal vertical cross-sections of AEC along two key latitudinal transects (38.0 and 40.0° N). These transects capture the transition from continental dust sources and anthropogenic centers to downwind marine regions. (1) Along the 38.0° N transect: CALIOP data (Fig. 9a) reveal two distinct high-extinction cores: the Taklamakan Desert (75–85° E) and the NCP (115–120° E). The original GEOS-Chem model (Fig. 9c) almost completely fails to capture the intense near-surface dust accumulation in the Taklamakan region – likely due to uncertainties in dust emission schemes or terrain smoothing effects in the CTM – and severely underestimates the core intensity over the NCP. The GC-TF model (Fig. 9e) successfully recovers the missing dust signal and sharpens the anthropogenic core over the NCP, restoring high extinction values (>0.16 km⁻¹) within the 0–1 km layer to match observations. (2) Along the 40.0° N transect: This profile highlights model performance over Northeast Asia and the Sea of Japan. CALIOP detects a concentrated high-extinction core over North Korea (∼127° E). While the original model (Fig. 9d) significantly underestimates this peak, the GC-TF (Fig. 9f) effectively captures this local anthropogenic hotspot. Notably, the original GEOS-Chem exhibits unphysical aerosol “blobs” over the Sea of Japan (135–138° E) and near 148° E, which are unsupported by observations. The GC-TF model effectively suppresses these model artifacts, ensuring that the extinction distribution in the downwind marine regions maintains physical consistency with CALIOP observations.

Figure 10 presents a comprehensive evaluation of the GC-TF model's performance in correcting column-integrated AOD biases over both the primary study domain (EA) and an independent generalization domain (NA). By comparing CALIOP observations, original GEOS-Chem simulations, and the GC-TF model results, we elucidate the model's efficacy in reproducing spatial heterogeneity and improving statistical consistency.

Within the EA training domain, although the original GEOS-Chem simulation (Fig. 10a2, b2, c2) captures the macroscopic features of aerosol distribution, it exhibits significant systematic biases. Specifically, it tends to underestimate AOD intensity over major anthropogenic source regions (the NCP and the IGP) and biomass burning hotspots (the Indochina Peninsula), while simultaneously introducing spurious background aerosols over the cleaner Tibetan Plateau and Western Pacific. In contrast, the GC-TF model (Fig. 10a3, b3, c3) significantly sharpens spatial gradients. The corrected AOD fields show high agreement with CALIOP observations (Fig. 10a1, b1, c1), effectively recovering high-value centers in polluted regions while suppressing false positives in clean areas. Statistical evaluation further confirms this improvement: while the original simulation shows dispersed scatter plots with low slopes (0.65–0.74), the GC-TF corrected data tightly converge onto the 1:1 identity line. The R improves from 0.80–0.84 to 0.91–0.93, the RMSE decreases by approximately 26 %–40 %, and the regression slope recovers to 0.82–0.99 (Fig. 10a5, b5, c5). The temporal consistency observed from 2017 to 2019 indicates that the model has learned stable physical mapping relationships rather than overfitting to specific meteorological years.

Crucially, the evaluation over the NA domain (Fig. 10d) provides compelling evidence of the model's spatial generalization capability. Despite the significantly lower AOD magnitude and distinct emission characteristics compared to EA, the GC-TF model demonstrates robust transferability. The original GEOS-Chem simulation over NA (Fig. 10d2, d4) shows poor agreement with observations (R=0.31, slope = 0.18), indicating severe deficiencies in capturing regional aerosol variability. Specifically, it underestimates anthropogenic pollution sources in the Eastern US (Fig. 10d1) and exhibits spurious high-AOD trails over the Gulf of Mexico and the East Coast, likely due to excessive transport or overestimated sea salt. Applying the GC-TF model – trained exclusively on EA data – to this unseen region (Fig. 10d3, d5) yields a substantial performance leap: R more than doubles to 0.70, and the slope improves to 0.45. Spatially, the model successfully recovers the smoothed pollution peaks in the Eastern US and corrects the oceanic regions to clean background levels, consistent with CALIOP. This bidirectional correction capability – enhancing underestimated terrestrial signals while suppressing overestimated oceanic backgrounds – strongly suggests that the physics-informed Transformer framework has captured the universal physical linkages between atmospheric states and simulation biases, rather than merely memorizing the geographical features of the EA training domain.

To understand how the model resolves 3D aerosol fields, we first examine its overarching reliance on different information streams. Domain-wide permutation feature importance (Fig. S15) unambiguously establishes the foundational role of physical priors: randomly permuting the physicochemical profile induces a dramatic 196.1 % increase in MSE. This confirms that the physicochemical profiles provided by the CTM remain the indispensable physical foundation, determining the absolute Magnitude of the AEC. In contrast, spatial, temporal, and height components function as modulating variables, refining this baseline across diverse environmental regimes.

Further analysis of the gated feature fusion weights (Fig. 12) reveals that the model effectively adapts its prioritization mechanism based on atmospheric stratification. In the near-surface layer (<0.5 km), the model assigns the highest weight to physicochemical profiles, aligning with the physical reality that extinction near the surface is predominantly controlled by local emissions and immediate thermodynamic states (Jiang et al., 2024; Xiong et al., 2026). As height increases to the boundary layer transition zone (0.5–1.0 km), a strategic shift occurs. The reliance on physicochemical profiles diminishes while the weight of spatial coordinates increases significantly. This region typically corresponds to the entrainment zone or the top of the PBL, where CTMs are prone to vertical diffusion errors (Eastham and Jacob, 2017; Rastigejev et al., 2010; Lin and McElroy, 2010). The model mitigates these uncertainties by leveraging spatial priors to constrain potential diffusion biases. In the mid-lower troposphere (1.0–3.5 km), the contribution of temporal indices exhibits distinct peaks around 1.5 and 2.8 km. The 1.5 km peak corresponds to the typical maximum daytime PBLH in EA (Guo et al., 2016; Kim, 2022), while the 2.8 km peak aligns with the active layer for long-range transport (Uno et al., 2009). This demonstrates the model's utilization of temporal cues to capture the diurnal evolution of the PBL and seasonal transport events. In the free troposphere (>3.5 km), aerosol variability is vertically decoupled from surface processes and driven primarily by large-scale advection (Weinzierl et al., 2017; Val Martin et al., 2013; Uno et al., 2009). The model successfully captures this decoupling, shifting its strategy to rely heavily on spatial coordinates to constrain background aerosol fields. Explicit height encoding maintains a consistently high contribution throughout the entire column, serving as a critical vertical positioning anchor.

Following the domain-wide ranking, we utilize gradient-based attribution (Fig. 13) to dissect the specific variables within the VPS driving AEC bias correction across altitudes. These drivers are organized into thermodynamic constraints, particulate compositions, and dynamic factors.

First, thermodynamic variables serve as the primary constraints for rectifying the vertical AEC structure. Temperature (T) consistently acts as the dominant driver within the PBL, with attribution scores exceeding 0.20. This suggests that the model implicitly diagnoses atmospheric stability and vertical lapse rate – factors often mischaracterized in CTMs – to rectify biases associated with turbulent mixing (Lin and McElroy, 2010). Concurrently, Relative Humidity (RH) functions as a critical driver for aerosol optical properties. Its contribution is coupled with explicit hygroscopic growth factors (e.g., AerHygroscopicGrowth_SO42-), enabling the model to fine-tune the AEC and correct non-linear hygroscopic parameterization errors under high-humidity conditions (Burgos et al., 2020; Zhai et al., 2021).

Second, particulate mass concentrations act as the fundamental determinants of aerosol loading. In the lower troposphere (<1.5 km), PM_2.5 and PM₁₀ consistently rank among the top drivers. The model also demonstrates a physically stratified recognition of aerosol types; for instance, the importance of sea salt aerosol (AerMassSAL) is confined strictly to the marine boundary layer (<1.5 km) and decays rapidly aloft, accurately reflecting the vertical distribution of coarse-mode marine aerosols (Bian et al., 2019; Murphy et al., 2019).

Finally, dynamic variables exhibit a persistent influence aloft. Unlike precursor concentrations, which decay sharply with height, the importance of wind components (U, V) remains relatively stable in the free troposphere (>2.0 km). This indicates that as height increases, the model shifts its focus from local accumulation to large-scale advection, utilizing wind fields to rectify background biases induced by long-range transport.

While the VPS determines the baseline extinction, the cross-attention mechanism enables the model to utilize the SFS to modulate the vertical bias correction (Fig. 14). This process operates through distinct physical pathways.

First, the model employs a robust dynamic representation to constrain transport and mixing efficiency. The consistently high attention weights of 10 m wind components (U10M, V10M) reflect the use of near-surface wind speed as a proxy for synoptic flow patterns. The model identifies the dominance of meridional transport in the EA monsoon region, assigning slightly higher importance to meridional winds (V10M) to capture dominant pollutant exchange pathways (Ding et al., 2009; Choi et al., 2024; Uno et al., 2009). By identifying prevailing dynamic regimes, the model effectively addresses CTM biases related to pollutant accumulation under stagnant conditions (Kim et al., 2024; An et al., 2019) and numerical diffusion under strong advection (Rastigejev et al., 2010; Eastham and Jacob, 2017). More critically, the cross-attention weights reveal a vertical partitioning of turbulence drivers. Thermodynamic drivers (HFLUX, LAI) peak at the surface and decay upward, diagnosing surface buoyancy fluxes. In contrast, mechanical drivers (USTAR, Z0M) increase and plateau with height. This distinction implies the model successfully evaluates vertical entrainment potential, assessing whether mechanical shear is sufficient to transport pollutants across capping inversions.

Second, radiative and surface boundary conditions are leveraged to correct parameterization biases. The model senses solar input by distinguishing between direct (PARDR) and diffuse (PARDF) photosynthetically active radiation, capturing variations in photochemistry and secondary aerosol formation (Guenther et al., 2012). Furthermore, snow mass (SNOMAS) emerges as a key predictor in the lowest layers. The model identifies snow-covered surfaces as indicators of a strongly stable boundary layer prone to temperature inversions. This allows for the targeted correction of over-dilution biases often found in CTMs (Lin and McElroy, 2010; Holtslag et al., 2013), effectively capturing high-concentration signals that are typically artificially smoothed by minimal diffusion threshold constraints.

To reveal the model's predictive behavior under diverse environmental contexts, we conduct SHAP analysis (Fig. 15) to identify region-specific correction patterns adapted to distinct underlying surfaces and emissions.

In regions dominated by anthropogenic and biomass burning emissions (NCP, IGP, and Indochina), the model leverages radiative components to diagnose atmospheric turbidity. A striking commonality is the high ranking of diffuse radiation (PARDF), often surpassing the direct component (PARDR). This reflects the physical phenomenon where high aerosol loading enhances scattering and increases the diffuse fraction of solar radiation (Mercado et al., 2009; Che et al., 2018). Furthermore, the model differentiates surface energy partitioning: in the humid, vegetated IGP and Indochina, it prioritizes latent heat flux (EFLUX) to gauge hygroscopic growth and wet removal potential; conversely, in the urbanized NCP, it relies more heavily on sensible heat flux (HFLUX), consistent with the high Bowen ratio of urban surfaces (Miao et al., 2009) where thermal turbulence dominates vertical dispersion.

In the dust-dominated Taklamakan Desert, the model captures a coupled mechanism driven by thermodynamic instability and dynamic uplift. Incident shortwave flux (SWGDN) and direct radiation (PARDR) play a dominant role, indicating that the model identifies clear-sky, high-solar-input conditions as prerequisites for thermal instability. Crucially, this is coupled with dynamic descriptors: combining low vegetation indices (GRN, identifying erodible bare soil), high 10 m wind speeds (providing surface shear stress) (Shao et al., 2011), and a preference for coarse-mode PM₁₀ over PM_2.5. This confirms the model has learned the physical prerequisites for wind-driven dust emission in arid regions.

Finally, over the marine environment of the Western Pacific, the model shifts to a latent heat-driven mode. Latent heat flux (EFLUX) defines the moisture supply at the air-sea interface, controlling marine aerosol hygroscopicity. Additionally, the model captures sea spray generation by linking near-surface wind speeds (V10M) with land-sea masking indicators (GRN), recognizing that mechanically generated sea salt aerosols (Grythe et al., 2014) and their subsequent hygroscopic evolution are the primary drivers of AEC variability over open water.

The model heavily relies on temperature and HFLUX to correct AEC profiles (Sect. 4.5.2, 4.5.4), which suggests potential uncertainties in diagnosing PBLH and turbulent mixing intensity within the GEOS-Chem non-local boundary layer scheme. Given that HFLUX drives surface buoyancy and directly modulates the vertical eddy diffusion coefficient, the widespread excessive diffusion biases observed in the lower troposphere indicate that the model may overestimate thermal turbulence under certain stability conditions. In highly urbanized regions like the NCP, the acute sensitivity to HFLUX implies that current surface energy balance calculations struggle to resolve the distinct thermodynamic properties of urban canopies. Future model development could benefit from constraining stability functions within the vertical diffusion module or coupling a dedicated urban canopy model to better represent sensible heat partitioning.

The cross-attention weights, which reveal how synoptic forcing modulates vertical aerosol profiles (Sect. 4.5.3, 4.5.4), highlight potentially inadequately parameterized mechanisms in current emission and chemical modules. Over the Taklamakan Desert, the model explicitly pairs greenness fraction with surface wind speed to capture dust extinction. This suggests that the GEOS-Chem dust emission scheme might struggle to accurately parameterize threshold friction velocity over complex bare soils, indicating that the non-linear response of wind-blown dust to surface shear stress and soil erodibility likely requires recalibration. Similarly, high sensitivity to diffuse radiation in the biomass burning region of Indochina points to potentially under-represented SOA formation. Given that high aerosol loading enhances diffuse radiation and alters photolysis rates, the data-driven model likely leverages diffuse radiation as a proxy for accelerated photochemical aging. This highlights a need to optimize SOA yield parameterizations and refine biomass burning plume injection heights to capture rapid aerosol evolution in dense smoke.

Beyond statistical bias correction, this study highlights the utility of physics-informed DL for model diagnosis. By decoupling the contributions of meteorology and aerosol composition, the framework verifies that CTMs provide a robust physicochemical baseline, yet exhibit uncertainties in representing the complex, non-linear interactions between aerosols and meteorology. The correction strategies derived from the data-driven model offer valuable diagnostic clues. Identifying specific environmental proxies that govern simulation biases bridges the gap between data-driven retrieval and deterministic modeling, ultimately guiding the targeted integration of neglected physical constraints into future parameterization schemes.