The σbsc,532 data for deep learning module training and PM_2.5 chemical component retrieving is obtained from a ground-based dual-wavelength polarization Mie lidar at the Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences (CAS), Beijing (39.98° N, 116.38° E). This Mie lidar has consistently detected optical signals since 2017, offering a temporal resolution of 15 min and a vertical resolution of 6 m. The lidar specification parameters and data preprocessing are detailed in Sect. S1 (and Table S1) and Sect. S2 in the Supplement, respectively. The σbsc,532 data from 8–15 February 2021 at 23 lidar sites in the North China Plain (NCP), provided by the China National Environmental Monitoring Center (CNEMC), were utilized to assess the spatial generalization ability. The multi-site data offers a temporal resolution of 5–20 min and a vertical resolution of 7.5 m. To generate an hourly resolution lidar dataset, minute-level data were resampled using a simple averaging method. Specifically, the arithmetic mean was calculated from all valid minute-level data points within each non-overlapping one-hour window aligned to the start of each hour (e.g., from 00:00 to 00:59).

The data of multiple meteorological parameters for deep learning module training and PM_2.5 chemical component retrieving can be obtained from the 5th Generation European Centre for Medium-Range Weather Forecasts (ECMWF) ReAnalysis (ERA5, https://cds.climate.copernicus.eu/datasets, last access: 25 July 2025), which provides the hourly data on pressure levels (1000–1 hPa) from 1940 to present with a spatial resolution of 0.25°×0.25°. The data of fine soil, coarse mass and fine sea salt for physics-constrained optimization can be obtained from 4th Generation ECMWF Atmospheric Composition Reanalysis (EAC4, https://ads.atmosphere.copernicus.eu/datasets, last access: 25 July 2025), which provides the 3 h data on pressure levels (1000–1 hPa) from 2003 to 2024 with a spatial resolution of 0.75°×0.75°. The mass concentration (µg m⁻³) of fine soil is approximately estimated by the mixing ratio (kg kg⁻¹) of dust aerosol with a diameter of 0.03–0.9 µm. The mass concentration (µg m⁻³) of coarse mass is approximately estimated by the mixing ratio (kg kg⁻¹) of dust aerosol with a diameter of 0.9–20 µm. The mass concentration (µg m⁻³) of fine sea salt is approximately estimated by the mixing ratio (kg kg⁻¹) of sea salt aerosol with a diameter of 0.03–5 µm. The pressure levels (hPa) of ERA5 and EAC4 are converted to geometric heights (m), and the 3 h EAC4 data is converted to hourly data through a linear interpolation method. The grid cells of EAC4 and ERA5 that contain the lidar sites were extracted using the k-nearest neighbor search method based on longitude and latitude data (Friedman et al., 1977). The lidar data and the reanalysis data were interpolated onto a preset vertical grid with a height range of 50 m to 3 km using linear interpolation. The preset height information is presented in Sect. S2.

Ground-level mass concentrations of NH4+, SO42-, NO3-, OM and BC at the Beijing lidar site (39.98° N, 116.38° E) were collected for training the deep learning module and validating retrievals by a high-resolution time-of-flight aerosol mass spectrometer, with a temporal resolution of 1 h, covering the periods from 1 January 2021, to 31 March 2022, and 1 June to 31 August 2022. Ground-level mass concentrations of the five PM_2.5 chemical components at 23 non-training NCP sites were provided by CNEMC. Besides, ground-level PM_2.5 mass concentrations, approximately equal to the sum of the mass concentrations of the five chemical components, are available on CNEMC data release website (https://www.cnemc.cn/, last access: 25 July 2025).

The aircraft-based vertical profiles for retrieval independent verification were sampled in a flight experiment at an airport site in Shijiazhuang (37.54° N, 114.35° E). The flight time schedules (LT, local time) are detailed in Table 1. The tower-based vertical profiles at altitudes of 16, 102 and 280 m were sampled at a 325 m meteorological tower located at the IAP, CAS in Beijing (39.98° N, 116.38° E) for 10 d (27 and 30 December 2023; 2, 5, 9, 12, 15, 18, 24, and 27 January 2024). A flow sampler with a flow rate of 42.8 L min⁻¹ and the 47 mm quartz filter membranes were utilized to collect PM_2.5 chemical component samples in the aircraft-based and tower-based sampling experiments. Furthermore, the 325 m tower-based vertical profiles from 30 December 2018 to 2 January 2019 were also collected from Lei et al. (2021)'s study.

This paper proposed a novel retrieval framework for retrieving the vertical concentration profiles of five PM_2.5 chemical components (NH4+, SO42-, NO3-, OM and BC) from the lidar aerosol extinction coefficient at 532 nm (σbsc,532). As shown in Fig. 1, the retrieval framework mainly consists of a deep learning module and a physics-constrained optimization module. The input datasets of the deep learning module include the surface observation data, meteorological data and ground-based lidar data (Fig. 1a). Specifically, the aerosol extinction coefficient at 532 nm (σbsc,532) and multiple meteorological parameters (u-component wind, v-component wind, temperature, relative humidity, specific humidity, vertical velocity and geopotential) serve as input features, while the concentrations of the five PM_2.5 chemical components (NH4+, SO42-, NO3-, OM and BC) serve as target features. The deep learning module (Fig. 1b), mainly consisting of the Convolutional Neural Network (CNN), Bidirectional Long Short-Term Memory (BiLSTM), attention mechanism and Bayesian optimization, is utilized to establish the nonlinear relationship between input and target features. The input datasets of the physics-constrained optimization module include the ground-based lidar data, aerosol auxiliary data and deep learning intermediate output (Fig. 1a, c), which provide fundamental input for establishing a multi-object function based on the Interagency Monitoring of Projected Visual Environment (IMPROVE) equation. The physics-constrained optimization module incorporates the multi-object loss function with the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to implement external physical constraints (Fig. 1c), thus enhancing the extrapolation capability of the deep learning module and generating high-quality vertical concentration profiles of the five PM_2.5 chemical components. Detailed descriptions of the deep learning algorithms, hyperparameter tuning, and physics-constrained optimization used in this work will be presented in subsequent sections. The brief workflow of the retrieval framework is summarized as follows.

Step 1. The multi-source input datasets undergo matching across spatiotemporal and vertical dimensions. All input and output data are uniformly time-resolved to hourly intervals, while vertical data are uniformly vertically resolved into 10 layers ranging from 50 m to 3 km.

The deep learning module is the core of the retrieval framework that generates the normalized vertical profiles of five PM_2.5 chemical components by feeding the lidar-based aerosol extinction coefficient at 532 nm (σext,532) and multiple meteorological parameters. The deep learning module is designed by numerous neural network layers (Fig. 1, red part), including the CNN layer, Average Pooling layer, Rectified Linear Unit (ReLU) layer, Fully Connected (FC) layer, Attention Mechanism layer, Sigmoid layer, Flatten layer, BiLSTM layer, Dropout layer and Regression Output layer. The CNN and BiLSTM layers, coupled with the Attention Mechanism (AM), are designed to effectively capture the multivariate and temporal characteristics in the training data, thereby establishing a robust nonlinear mapping between the input and output features. The hybrid CNN-BiLSTM-AM architecture consistently outperforms single-architecture models in predictive tasks, as evidenced by numerous studies (Kavianpour et al., 2023; Ma et al., 2022; Shan et al., 2021; Zhang et al., 2023). Other layers are responsible for data input, structural transformation, normalization, nonlinear process, pooling process, neuron removal and data output, enhancing the training performance and preventing overfitting. Here, we review the description of three key layers, and the description of other layers can be found in our previous work (Li et al., 2025a).

CNN is a variant of the multilayer perceptron that efficiently identifies the relevant features through local perception, sparse connections and sharing of weight and bias (Alzubaidi et al., 2021). The convolutional layer in CNN performs convolutional computation on input across spatial dimensionality using learnable kernels to extract local features and enhance training efficiency (O'Shea and Nash, 2015). Then the convolutional output is typically enhanced nonlinearly by the ReLU layer (Eq. 1) or down-sampled nonlinearly by the pooling layer in a CNN architecture. 1yt=max0,fw×xt+bt, where yt is the nonlinearly enhanced convolutional output at timestep t, fw×xt+bt is the original convolutional output at timestep t, xt is the input data at timestep t, w is the weight vector and bt is the bias term.

The attention mechanism layer is incorporated with CNN to amplify the weight of key information and mitigate the interference of redundant information, leading to an enhancement in the quality of the CNN output (Wang and Zhang, 2025). The attention mechanism is inspired by the ability of human vision to selectively focus on key information (Guo et al., 2022). Our retrieval framework integrates a data-driven channel attention mechanism, which rescales the original feature channels from the convolutional layers through element-wise multiplication using learned attention weights, thereby enhancing the importance of key features and reduce the interference of irrelevant features. The attention weights are generated by the FC layers with a sigmoid activation function (Eq. 2) and then performs Schur product operation with CNN multivariate output (Eq. 3). 2W=sigmoidFCPoolingy1,i,3y2,i=W⋅y1,i, where y1,i is the CNN multivariate output. Pooling and FC layers are responsible for down-sampling and feature learning, respectively, thus predicting the importance of ith feature. The sigmoid activation function is utilized to calculate the attention weight (W). y2,i is the reweighted multivariate output.

BiLSTM is a variant of Recurrent Neural Networks (RNNs) that learns long-timestep information bidirectionally and avoids the gradient vanishing or explosion of traditional RNNs (Kavianpour et al., 2023). Previous studies have indicated that BiLSTM outperforms LSTM in regression tasks due to the insufficient utilization of future information in LSTM (Siami-Namini et al., 2019; Yang and Wang, 2022). Therefore, the BiLSTM layer is integrated into the deep-learning module to fully capture the temporal characteristics of the CNN attention-weighted multivariate output. The BiLSTM layer is realized by the forward LSTM and backward LSTM (Eq. 4). Both the forward and backward LSTM consist of cell states, forget gates, input gates, output gates, and activation functions, which are responsible for transmission, screening and processing of temporal information. The final LSTM output is obtained by output gates and cell states (Eq. 5). A detailed description of BiLSTM components can be found in our previous work (Li et al., 2025a). 4Ht=h→t;h←end-t+1,5ht=ot×tanh⁡(Ct), where Ht is the final output of BiLSTM at timestep t, which is obtained by concatenating the forward output ht and backward output value h←end-t+1. ht is the final output of LSTM at timestep t, ot is the output of output gate at timestep t, tanh is an activation function that regulates the values transmitted in neural networks by compressing the values to a range of from -1 to 1. Ct is the output of the cell state at timestep t.

Hyperparameter tuning is crucial for improving the performance of deep neural networks. Bayesian optimization can determine global optima with higher efficiency (Shahriari et al., 2016) and has been widely employed in hyperparameter optimization of varying machine learning models (Wu et al., 2019a). The primary process of Bayesian optimization involves establishing search spaces for hyperparameters and the corresponding objective function, followed by the determination of the optimal solution by minimizing the objective function (Eq. 6). Bayesian optimization utilizes a probabilistic surrogate model to iteratively estimate the complex unknown objective function based on the current query point and then identifies the next most promising query point by an acquisition function (Shahriari et al., 2016). The probabilistic surrogate model and the acquisition function in this study are the Gaussian process regression model (Rasmussen, 2004) and the Expected-Improvement-Per-Second-Plus function (Gelbart et al., 2014), respectively. The number of optimization iteration is set to 30 and the final optimal settings of model hyperparameters are presented in Table S2. 6x∗=argminf(x),x∈X⊆Rd, where x∗ is the optimal scheme of multiple hyperparameters, x is the decision vector composed of d-dimensional hyperparameters, X is the search space that consists of all possible decision vectors, f(x) is the unknown objective function.

The normalized vertical profiles of PM_2.5 chemical components generated by the deep learning module are denormalized by the statistical characteristics of the initial input data of the surface-level observations. To reduce the retrieval error induced by the inherent extrapolation limitations of deep learning modules, a physics-constrained optimization scheme is incorporated into the retrieval framework based on a revised Interagency Monitoring of Projected Visual Environment (IMPROVE) Equation (Pitchford et al., 2007) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) (Verma et al., 2021).

The revised IMPROVE Equation interprets the particle extinction coefficient (σ) through the concentrations (M) and the optical and microphysical characteristics of PM_2.5 chemical components (Eq. 7). 7σ(M)=θsSNAfRH(M(SO42-)+M(NO3-)+M(NH4+))+θsOCM(OC)+θsFSM(FineSoil)+θsCMM(CoarseMass)+θsFSSfFSSRHM(FineSeaSalt)+θaBCM(BC)+RayleighScattering, where σ(M) is the estimated particle extinction coefficient (km⁻¹), θs is the scattering efficiency (m² mg⁻¹), θa is the mass absorption efficiency (m² mg⁻¹), respectively. fRH and fFSSRH account for the increase in light scattering induced by hygroscopic growth of sulfate, nitrate and ammonium (SNA), as well as fine sea salt (FSS). θsFS, θsCM, θsFSSfFSS and θaBC are set to 0.001 m² mg⁻¹, 0.0006, 0.0017 and 0.01 m²,mg⁻¹, respectively. M are the mass concentrations (µg m⁻³) of the PM_2.5 chemical components. Rayleigh Scattering is set to 0.01 km⁻¹. θsSNA and θsOC are determined by Eqs. (8)–(9). 8θsSNA=0.003×(0.7+0.002×(M(SO42-)+M(NO3-)+M(NH4+)+M(OC))),9θsOC=0.00363×(0.7+0.002×(M(SO42-)+M(NO3-)+M(NH4+)+M(OC))), To implement the physics-constrained optimization, we first introduce a scale factor (γi,h) for each chemical component at each vertical layer, which is used to correct the initial mass concentrations (Eq. 10). Then we determine the optimal scale factors through minimizing a multi-objective function (Eq. 11). The Pearson correlation coefficient (CORR) and root mean square error (RMSE) quantified by the lidar-observed and the IMPROVE-simulated extinction coefficient serve as two objective values in the multi-objective function. The NSGA-II algorithm is utilized to determine the optimal scale factors by solving the multi-objective function that simultaneously enhances the correlation and reduces the discrepancy between the IMPROVE-estimated and lidar-observed extinction coefficients. 10Mregulatedi,h=γi,h×Moriginali,h,i=SO42-NO3-,NH4+,OM,andBC,11γi,h=min(fRMSEγ,fCORRγ), where Mregulatedi,h (µg m⁻³) is the regulated mass concentration of the ith chemical component at an altitude of h (m), γi,h is the scale factor for the ith chemical component at an altitude of h (m), and Moriginali,h (µg m-3) is the original mass concentration of the ith chemical component at an altitude of h (m). fRMSEγ is the RMSE-based objective function (Eq. 12) and fCORRγ is the CORR-based objective function (Eq. 13). 12fRMSEγ=∑k=1Kσkobs-σk(γ×M)2K,13fCORRγ=-∑k=1Kσk(γ×M)-σ(γ×M)‾SD(σ(γ×M))σkobs-σobs‾SD(σobs)K-1, where K is the total number of samples, σkobs is the kth observed extinction coefficient, σk(γ×M) is the kth simulated extinction coefficient, σ(γ×M)‾ is the average of simulated extinction coefficient, σobs‾ is the average of observed extinction coefficient, SD(σ(γ×M)) is the standard deviation of simulated extinction coefficient, and SD(σobs) is the standard deviation of observed extinction coefficient.

NSGA is capable of simultaneously optimizing the multi-objective function by generating a Pareto front that consists of an ensemble of non-dominated solutions (Srinivas and Deb, 1994). The non-dominated solutions in a Pareto front meet the criterion that one objective cannot be further improved without compromising other objectives. However, the initial version of NSGA has several limitations. First, NSGA has a high computational complexity of OMN3, where M is the number of objective functions, and N is the size of the population. Second, NSGA utilizes a sharing parameter to preserve the diversity of the population that dominates the choice of Pareto non-dominated solutions, resulting in the introduction of parameter uncertainty into the algorithm. Third, NSGA lacks an elitism mechanism, leading to the incorrect removal of advantageous solutions. NSGA-II is an improved NSGA with a lower computational complexity of OMN2 and an elitism mechanism that retains the dominant members of the parent and offspring generations during iterative evolution (Deb et al., 2002). Moreover, NSGA-II replaces the sharing parameters in NSGA with the crowding distance operator, mitigating the uncertainty of sharing parameters and the high computational complexity of sharing functions.

NSGA-II implements multi-objective optimization by two primary procedures, namely non-dominated sorting and crowding distance calculation. The non-dominated sorting progressively identifies the Pareto front at each rank from a population of size N. The Pareto front at the second rank is derived from a population that excludes the Pareto front at the first rank. The crowding distance is utilized to quantify the priority of all optimal solutions within a Pareto front, defined as the normalized distance of two nearest optimal solutions on either side (Eq. 14). 14di=∑i=1Kfmi+1-fmi-1fmmax-fmmin, where di is the crowding distance of the ith intermediate Pareto optimal solution, K is the number of Pareto optimal solutions in a Pareto front, fmi+1 is the mth objective value induced by the (i+1)th Pareto optimal solution, fmi-1 is the mth objective value induced by the (i-1)th Pareto optimal solution, fmmax and fmmin are the mth maximum and minimum objective values, respectively.

The workflow of NSGA-II is summarized as follows (Fig. 2). a.

Randomly generating an initial population (A1) of size N. Performing selection, crossover and mutation operations on A1 to generate an offspring population (B1) of size N. The parent population (A1) and the offspring population (B1) are combined to form a new population (C1) of size 2N.

An hourly multivariate dataset with extensive temporal coverage was employed to train and evaluate the deep learning module. To maintain temporal independence, the training (and validation) set was constructed from a 1-year (2021) time-series dataset obtained from a Beijing site (Fig. S1), while the testing set contains an independent 6-month (1 January–31 March and 1 June to 31 August 2022) time-series dataset obtained from the same site. A 10-fold time-series cross-validation (CV) scheme was designed for the training (and validation) set to preserve its temporal order and prevent future information leakage, which is detailed in Sect. S3 and Fig. S2 in the Supplement. The iteration number of Bayesian optimization is set to 20.

To fully evaluate the performance of the retrieval framework in predicting vertical profiles of NH4+, SO42-, NO3-, OM and BC, we conduct three retrieval experiments: (1) We compare the retrieved mass concentrations with the observed values at the surface level during a training year (2021) and three non-training years (2017, 2018 and 2024) to validate the temporal generalization in all seasons and under diverse meteorological conditions. (2) We assess the spatial generalization ability by applying the retrieval framework to 23 non-training lidar sites in the NCP from 8–15 February 2021 and comparing the retrieved mass concentrations with observations at the surface level. The spatial distribution of the 23 non-training lidar sites is presented in Fig. S1. (3) We validate the retrieved vertical profiles by aircraft-based and tower-based vertical observations during several non-training episodes. Subsequently, SHapley Additive exPlanations (SHAP), a local explainable technology (Lundberg et al., 2020), has been widely employed in prediction interpretation for varying machine learning models (Li et al., 2025b; Hou et al., 2022), is integrated into the deep learning module to quantify the impact of multivariate input features on the retrieval of PM_2.5 chemical components. Finally, we applied this retrieval framework to generate a long-term vertical profile dataset for five PM_2.5 chemical components in a megacity over six years of 2017–2018 and 2021–2024.

The 10-fold CV sets and a testing set with temporal independence are utilized to evaluate the predictive performance of the deep learning module, which is quantified by the discrepancies between simulations and observations at ground level for NH4+, SO42-, NO3-, OM and BC. Overall, the scatter distribution and fitted regression line closely align with the 1:1 line in both the 10-fold CV (Fig. 3a1–a5) and temporally independent testing phases (Fig. 3b1–b5). The error distributions are concentrated around 0, with mean errors between -1.78±8.15 and -0.13±0.94 µg m⁻³ during the 10-fold CV phase (Fig. S3a1–a5) and between -1.36±7.40 and -0.07±1.00 µg m⁻³ during the temporally independent testing phase (Fig. S3b1–b5), demonstrating strong consistency between observations and simulations. Notably, the error distributions for the validation and independent testing sets are closely aligned, indicating that the deep learning module is robust and generalizes well to unseen data. Specifically for the 10-fold CV process (Fig. 3a1–a5), the CORR values for the five PM_2.5 chemical components range from 0.76 to 0.86, indicating that the deep learning module accurately interprets the relationship between multivariate input features and the five PM_2.5 chemical components. The RMSE values range from 0.95 to 8.35 µg m⁻³, indicating a low discrepancy between simulations and observations. Compared to the 10-fold CV process, the temporally independent testing yields slightly lower CORR values (0.69–0.79) and higher RMSE values (1.00–8.87 µg m⁻³), showing a slight underestimation for the five PM_2.5 chemical components (Fig. 3b1–b5). It is expected that the statistical results from the temporally independent testing are less robust than those from the 10-fold CV, since the temporally independent testing set aggregates a broader spectrum of temporal patterns compared to the validation set at each fold. Our statistical results from the 10-fold CV exhibit similarities or even improvements compared to those reported in other studies that predicting PM_2.5 chemical component concentrations based on machine learning models (Lv et al., 2021; Lin et al., 2022; Araki et al., 2022; Liu et al., 2023), indicating that the deep learning module demonstrates strong prediction capabilities.

The retrieval framework was applied to retrieve the vertical profiles of NH4+, NO3-, SO42-, OM and BC in a Beijing lidar site (39.98° N, 116.38° E) over a training year (2021) and three non-training years (2017, 2018 and 2024). As illustrated in Fig. 4a1–a5, the weekly-smoothed variations in the retrieved surface concentrations of the five PM_2.5 chemical components demonstrate strong consistency with the observed surface concentrations for the training year, indicating that the retrieval framework adequately captures the temporal characteristics of these chemical components. The CORR values between the retrieved and observed concentrations range from 0.87 to 0.97, surpassing those of the deep learning module (Figs. 4a1–a5 and 3b1–b5). In addition, the RMSE values for all five chemical components (0.57–4.98µg m⁻³) are consistently lower than those from the deep-learning module (Figs. 4a1–a5 and 3b1–b5). These results demonstrate that the physics-constrained optimization effectively enhances the retrieval accuracy of chemical component concentrations.

For the non-training years, the retrieved surface concentrations of a sum of five PM_2.5 chemical components are compared to the observed surface PM_2.5 concentrations, owing to the absence of long-term observations for individual chemical components. As shown in Fig. 4b–d, the weekly-smoothed variations in the retrieved surface PM_2.5 concentrations closely align with the observed values in 2017, 2018 and 2024. The high values of surface PM_2.5 concentration observed in March–April and November of 2018 and 2024 are effectively captured by the retrieval framework. These results indicate that the retrieval framework roughly interprets the changes in concentrations of various chemical components across different periods, exhibiting fundamental temporal generalization capabilities. However, the retrieved concentrations show some overestimation cases during autumn in 2018 and spring in 2024, potentially associated with the uncertainties induced by the training data. The training data may lack a sufficiently diverse spectrum of meteorological conditions and pollution patterns, which limits the temporal generalizability of the retrieval framework across all complex and dynamic atmospheric scenarios. Future efforts should enhance retrieval accuracy by augmenting the training data with observations spanning a wider range of temporal conditions.

The retrieval framework was also applied to retrieve the vertical profiles of the five PM_2.5 chemical components at 23 non-training NCP lidar sites over a short-term period of 8–15 February 2021, aiming to validate its spatial generalization capabilities. Compared with the observed surface concentrations at 23 non-training sites, the retrieved surface concentrations exhibit a more clustered data distribution and exhibit a tendency toward underestimation across all components (Fig. 5a). The site-averaged CORR values for the five chemical components range from 0.21 to 0.46, with RMSE values spanning 2.7 to 20.37 µg m⁻³ (Fig. S4). From a spatial perspective (Fig. 5b1–b5), non-training NCP sites located closer to the Beijing lidar site exhibit higher CORR values, with the highest reaching 0.71 (NH4+), 0.56 (NO3-), 0.81 (SO42-), 0.48 (OM) and 0.41 (BC). Conversely, the RMSE values are not affected by the distance from the Beijing lidar site (Fig. 5c1–c5), with the lowest reaching 2.91 µg m⁻³ (NH4+), 6.15 µg m⁻³ (NO3-), 3.05 µg m⁻³ (SO42-), 6.59 µg m⁻³ (OM) and 0.78 µg m⁻³ (BC). However, several sites exhibit poor retrieval performance, with CORR values ranging from ∼0.20 to ∼0.30 (Fig. S5), which is primarily attributed to limitations in the spatial representativeness of the training data. The deep-learning module was trained exclusively on a long-term dataset from a single site in Beijing, which is insufficient to capture the spatial variability in emission intensity, as well as local meteorological and geographical conditions across the broader NCP. As a result, the spatial extrapolation capability of the deep-learning module is constrained. Although the retrieval framework can retrieve PM_2.5 chemical component concentrations at spatially distributed lidar sites, future work should incorporate long-term datasets from varying locations to enhance spatial generalization and extrapolation performance.

In addition to the spatiotemporal verification of surface-level mass concentrations, tower-based and aircraft-based observational experiments were conducted to validate the retrieved vertical profiles of five PM_2.5 chemical components during non-training periods. From the surface to ∼200 m altitude, the retrieved and observed vertical profiles exhibit similar vertical patterns during a period from 30 December 2018 to 2 January 2019 in Beijing, with higher concentrations occurring at altitudes of 50–80 m for NH4+, NO3-, SO42- and OM (Fig. 6a1, a2). Specifically, as presented in Table S3, the CORR values are no less than 0.66 for all four PM_2.5 chemical components. However, the RMSE value for OM (23.04 µg m⁻³) is notably higher than that for the other components (4.08–10.48 µg m⁻³), indicating limitations in the retrieval framework when representing the vertical profile of OM during winter pollution episodes. This discrepancy may be associated with retrieval uncertainties arising from input data quality and imposed physical constraints. Additionally, the retrieved and observed proportions of NH4+, NO3-, SO42-, OM and BC demonstrate significant consistency (Fig. 6b1, b2). Among these chemical components, NO3- and OM contribute the largest proportions, followed by NH4+ and SO42-, while BC contributes the smallest fraction. This proportional characteristic is evident in both the retrieved and observed proportions at altitudes of 600 and 1200 m (Fig. 6c1, c2). Due to the lack of NH4+ measurements at 1500 m and the absence of both NH4+ and SO42- measurements at 2100 m, the proportions at these altitudes are statistically inferred from the remaining chemical components. The results indicate overall consistency between retrieved and observed proportions at altitudes of 1500 and 2100 m, although the proportion of NO3- is slightly overestimated at 2100 m and underestimated at 1500 m. Overall, the tower-based and aircraft-based verifications indicate that the retrieval framework achieves high accuracy in retrieving the vertical profiles of the five PM_2.5 chemical components during non-training period, demonstrating its robust generalization capability and reliability when applied to independent datasets.