Input variables of the deepWIA model includes daily averaged meteorological variables from the fifth-generation European Centre for Medium-range Weather Forecasts (ECMWF) reanalysis data (ERA5), with a horizontal resolution of 0.25∘×0.25∘. Since a trained DL model can automatically select the input variables to compose the best model that fits the target variable (PM2.5 concentrations) with activation functions, the task for feature engineering is to feed the DL model with as many variables as possible that are related to the day-to-day variation of PM2.5 concentrations. These input variables (Table 1) can be classified into four categories as follows.

Basic meteorological variables near the surface. We use 10 m altitude wind components, 2 m temperature, surface pressure, surface downward short-wave radiation, and total precipitation, which are frequently used as input variables in ML/DL-based studies of PM2.5 retrieval (Geng et al., 2021; Wei et al., 2020; Gui et al., 2020; Li et al., 2020). In addition, we introduce 100 m wind components and surface turbulent stress, as they are related to horizontal and vertical diffusion in the planetary boundary layer (PBL), respectively.

Meteorological fields in the upper air include geopotential height and temperature at 850 hPa. We introduce these two variables for the deepWIA model in learning the effects of synoptic patterns on aerosol variations.

Derived input variables referring to previous studies of aerosol concentration–meteorology relationships. Our model contains potential temperature and wet-equivalent potential temperature derived from PLAM, as they can identify the types of aerosol-related air masses controlling the local area (Yang et al., 2016). In addition, we introduce three kernel parameters of ASI, including ventilation potency, vertical diffusion potency, and wet deposition potency of aerosols (Feng et al., 2018). The ventilation potency illustrates the effects of wind speed in local PBL, which are simply represented by the nonlinear function of the height-weighted average of wind speed over the PBL; vertical diffusion potency is represented by the inverse of PBL height, which roughly presents the vertical diffusion range of aerosols due to turbulence; and wet deposition potency illustrates a significant decrease in the aerosol concentrations due to precipitation. The values of 0 and e correspond to precipitation greater than or equal to and less than 3 mm d-1, respectively. All the formulae for these variables derived from ASI are given in the Supplement (Eqs. S1–S3l). Moreover, referring to Porter et al. (2015), we use the daily maxima and minima of low-troposphere stability (i.e., the potential temperature difference between 700 hPa and the surface) and daily maxima of 2 m temperature and of 100 m wind speed.

Quasistatic and spatiotemporal variables (non-meteorological variables) include population density, surface altitude, and surface high vegetation cover, which are also commonly used in PM2.5 observation retrieval. The population density is regridded from the Gridded Population of the World (GPW) version 4 dataset at an original resolution of 1 km. Surface altitude and surface high vegetation cover are from the ERA5 datasets. These variables as well as latitude and longitude (Gui et al., 2020; Zhong et al., 2021) aid learning of the local characteristics of aerosol concentration. In addition, the model is built uniformly using all observed samples in China as the dataset (see Sect. 2.3). It is difficult for the model to obtain the correct seasonal information in the meteorological variables of these samples. Hence, we introduce seasonal information to the deepWIA model through a variable of “day of the year”, which has rarely been considered in previous models.

The fitting target of the deepWIA model is not the PM2.5 concentration per se but an index that tracks synoptic variations in PM2.5 concentrations. Motivated by the ASI and PLAM approaches, we use the predefined form 1r=C/B to separate the long-term background aerosol concentration, B, and synoptic variability, r, superimposed on B, where C is the daily averaged PM2.5 concentration. We term this process “timescale separation”. B is calculated as a 31 d running average over the current year and the previous year, i.e., 2B=162∑y-1y∑d-15d+15C, where d and y denote the date and year of the PM2.5 sample, respectively. The seasonality, the long-term trend in emissions and local characteristics of each sample are contained in B, and r, estimated from meteorological data, indicates the effect of weather on high-frequency variations in PM2.5 concentrations. It should be noted that the timescale of the running average is not a sensitive parameter for the performance of the deepWIA model. When a new model with the same structure, input variables, and training method as the original deepWIA model, but with a 61 d running average for the current year and the previous year as the background is used, the model performance is close to the original one using the background value with 31 d running averaged (see Fig. S1 in the Supplement).

Target data imbalance is an issue of concern. Previous studies have shown that PM2.5 concentrations have an extremely asymmetric long-tailed probability distribution function (PDF; Lu, 2002; Feng et al., 2018). The number of samples with low and medium values is much larger than that for high values (Fig. 1); r has a similar PDF, with values of 0–15, but concentrated mainly between 0 and 2. Such a distribution would weaken the performance of a data-based model, as it is difficult for such a model to discern small differences among low-value samples. To mitigate such data imbalance, the fitting target (i.e., the deepWIA, labeled r^) of our model is defined as 3r^=log⁡2r. This label transformation maintains the value of the target between -4 and 4 (Fig. 1c), giving a meaningful weather index for aerosol, with positive and negative values denoting aerosol-pollution days and clean days, respectively. For example, r^=+1 and -1 mean that the PM2.5 concentrations will be 2 times (i.e., 21) and 1/2 of (i.e., 2-1) the background concentration B, respectively.

National surface PM2.5 observations are from the real-time air quality platform (https://air.cnemc.cn:18007, last access: 3 August 2022) of the China National Environmental Monitoring Center. This platform has published air quality data since 2013. We use data from 2015 because the number of observation sites since that year exceeds 1000, with a widespread distribution across the country, making the sample more representative. Furthermore, the number of PM2.5 observation sites within different ERA5 grid cells is uneven, which would also undermine the representativeness of the sampling. Therefore, we use gridded observations, with the PM2.5 observation in a grid cell being the mean of all observations within that cell.

Aerosol concentrations at specific times and locations depend on local and surrounding meteorological fields over the current and past few days, as CTMs indicate. Therefore, we designed the deepWIA model as a spatiotemporal neural network (Fig. 2).

The spatial module of the model is based on residual network (ResNet; He et al., 2016). At each time step (i.e., day), the module can extract the information of the input variable and its spatial pattern within 9×9 ERA5 grid cells (about 200×200 km in China) around each observation sample point. We chose such a 9×9 sampling grid cell with reference to Feng et al. (2020b) and the limitations of our computational resources. The ResNet has a structure similar to that of the classical ResNet-50 (He et al., 2016), but only 49 convolution layers and a maximum of 512 channels (i.e., variables in convolution layers). These convolution layers of the ResNet automatically reorganize the input variables into multiple features associated with the target (i.e., PM2.5 concentrations). This ResNet does not have the final pooling (i.e., spatial average) layer of the original ResNet-50, because a sample over the 9×9 ERA5 grid cell has shrunk to a scalar spatially after 49 convolution layers. The number of channels is also less than the traditional ResNet-50 due to our computational resource limitation. And more channels do not provide better model performance. To be summarized, the ResNet module fuses meteorological and quasistatic variables around the sample points at each time step into multiple features.

The ResNet-extracted features are fed into the temporal module based on a gated recurrent unit (GRU) (Cho et al., 2014). The GRU is a recurrent neural network (RNN) that links the multiple features in a day-by-day order, combines the features together, and provides the final estimation of PM2.5 concentrations. Here, we consider a short 3 d GRU structure, with the exclusion of impacts of weather more than 3 d earlier. Unlike other applications of GRU, we do not use the output in every time step, except for the final day (Fig. 2), as we fit the deepWIA only on the last day. The GRU has learnable “gate” parameters that determine the extent to which features in previous days affect current aerosol concentrations. In other words, they would help the model understand aerosol accumulation–removal processes caused by weather changes. There is only 1 hidden layer with 1024 channels, and it is therefore computationally efficient. To summarize, GRU quantifies the influences of meteorology over 3 consecutive days and maps these influences on the PM2.5 concentrations on the final day.

Model outputs on the final day fit the target r^ for observation samples, using the mean squared error as the loss function.

We used ERA5 data and PM2.5 observations for 2015–2021 for training and validation. The number of training–validation samples was about 1.6 million. We selected the model using traditional 10-fold cross validation (CV), dividing training–validation samples randomly into 10 approximately equal parts, 9 of which were used for training and the remaining 1 for validation. To avoid model overfitting, the training process stopped when the loss function in the validation dataset did not decrease for several training epochs. Using every part as a validation dataset, the training–validation process was then repeated 10 times, generating 10 models. The RMSE for all validation datasets was used to select optimal hyperparameters such as learning rate, number of convolution channels, and batch size. Finally, retraining the entire training–validation dataset using these hyperparameters determined the final deepWIA model.

Both the deepWIA and the PM2.5 concentrations from Eqs. (1) and (3) were evaluated to illustrate model performance. We used five evaluation metrics in scatterplots, including the commonly used R2, RMSE, and mean absolute error (MAE). It is common for ML/DL-based models to underestimate high values and overestimate low values due to data imbalance (including in PM2.5 retrieval models). Therefore, we used biases in the ranges of r^<0 and r^>0 to evaluate model performance for clean and polluted weather, respectively. For PM2.5 concentrations (C), we used the ranges of C>35 µg m-3 and C<35 µg m-3, as 35 µg m-3 is the PM2.5 concentration limit of the China ambient air quality standard.

Figure 3 shows the fitting scatterplots of deepWIA and PM2.5 concentrations for the entire training–validation dataset. The r^ value had an RMSE of 0.45, an MAE of 0.34, and an R2 value of 0.58. The PM2.5 concentration had an RMSE of 16.91 µg m-3, an MAE of 9.5 µg m-3, and an R2 value of 0.76. Additionally, The DL model still underestimated high values and overestimated low values, although label transformation and some other processes were performed.

Scatterplots for the first validation dataset (Fig. 4) show slightly lower performance than that for the training set (RMSE = 0.49, MAE = 0.38, and R2=0.49 for r^; and 16.01 µg m-3, 9.67 µg m-3 and 0.70, respectively, for PM2.5 concentration), partly because of the smaller set of training samples than that used in final training. Validations in the other nine validation datasets had similar performance, as summarized in Figs. S2 and S3. The RMSE and R2 values for r^ for these validation datasets were in narrow ranges of 0.48–0.55 and 0.47–0.50, and the RMSE and R2 values for PM2.5 concentrations were 0.67–0.77 and 15.54–21.68 µg m-3, respectively. These metrics for 10-fold CV indicate no significant overfitting by the final deepWIA model and prove the stability of the model generated by the ResNet–GRU structure.

Once the DL model is established after training, a question worth discussing is the relative importance of these input variables. A DL model cannot answer by voting as the RF model. Therefore, here we perform sensitivity experiments to solve the problem: (1) for every input variable shown in Table 1, we deactivate it by setting all related model parameters to zero in the first convolutional layer; (2) we apply the modified model (i.e., without the effect of the given variable) to the training dataset and compute the RMSE of deepWIA; (3) we compute the difference between the RMSE and that of the original model. The larger the RMSE increases, the more important the input variable is. We applied these steps to all input variables and showed their importance rankings in Table 1. The five most important variables are latitude and longitude, 2 m mixing ratio, population density, maximal 2 m temperature, and surface turbulence stress components. However, some variables take little effect on the model (with an RMSE increase of less than 0.001), including wet deposition potency, precipitation, geopotential height at 850 hPa, ventilation potency, downward short-wave radiation, low cloud cover, and high vegetation cover.

Nevertheless, it would not be fair to compare the contribution of individual input variables to the DL model because there are overlaps in the contribution of several variables, such as 100 and 10 m winds. Therefore, we grouped all variables into six groups, namely near-surface wind variables, near-surface temperature-humidity variables, near-surface vertical diffusion variables, spatiotemporal geographic variables, synoptic pattern and radiation variables, and precipitation variables (Table S1 in the Supplement). Using the same approach as the individual variable, we compute the importance of each group of variables. The most important group is the spatiotemporal geographic variable, followed by the vertical diffusion and near-surface wind variables. The least important one is precipitation (Fig. S4).

Although the deepWIA appears accurate and robust in capturing synoptic variations in PM2.5 concentrations, it is of interest to investigate the reason for its strong performance. The model has three key points: (1) a ResNet–GRU structure with more meteorological variables; (2) a timescale separation approach making the model focus only on the effects of meteorology on synoptic variations in PM2.5 concentrations; and (3) a label transformation approach based on a logarithmic function to mitigate data imbalance. To investigate the relative importance of these processes for the final deepWIA model, two additional ablation experiments were performed for comparison:

AbExp_1: with fitting of PM2.5 concentrations directly using the same ResNet–GRU structure, samples, and training strategy, but with no timescale separation or label transformation. This experiment was similar to studies of ML-based PM2.5 concentration retrieval but using meteorological variables as primary data. This experiment was intended to assess the basic fitting power due to the DL structure and input variables.

Scatterplots of PM2.5 concentrations for AbExp_1 and AbExp_2 using the same test dataset as that used for the deepWIA model are shown in Fig. 8. The AbExp_1 experiment had an RMSE of 19.18 µg m-3, an MAE of 12.9 µg m-3, and an R2 value of 0.63, achieving the level of ML-based PM2.5 concentration retrieval (Sect. 4.2). The DL structure and the feature engineering for input variables thus builds a solid foundation for the fitting power of the deepWIA model. Compared with AbExp_1, AbExp_2 improved the R2 value to 0.70, with the RMSE decreasing to 17.13 µg m-3 and the MAE to 10.92 µg m-3, indicating the importance of timescale separation. Furthermore, the focus on synoptic variation also helped mitigate the overestimation of low values and underestimation of high values. The final deepWIA model further improved the general performance in estimating PM2.5 concentrations, with improved R2, MAE, and RMSE values. The logarithmic function-based label transformation mitigated the overestimation of low values while exacerbating the underestimation of high values, with this treatment increasing the distance between low values but decreasing the distance between high values of the samples. A scheme such as AbExp_2 may therefore be applicable to studies of extreme haze events. To summarize, model and feature engineering are most important in determining the final performance of the deepWIA model, with timescale separation and label transformation following in that order.

Recent studies of PM2.5 concentration retrieval use ML/DL models such as RF, XGB and MLP (Table 2). Unlike our model, these studies were not concerned with the role of meteorology but only with the accuracy of estimated PM2.5 concentrations. There are many differences between these methods and the deepWIA model in the model-building processes. For example, (1) the deepWIA model uses timescale separation to focus on synoptic variations in aerosol concentrations caused by meteorology. We do not use an emission inventory as an input feature for the model because of its significant uncertainty. It is difficult for DL models, which rely heavily on input data, to build robust relationships among emissions, meteorology, and aerosol concentrations. (2) Except for the approach of Geng et al. (2021), the training sample size used in deepWIA is much larger than that used in previous models, which often used data of 1 year for training (Geng et al., 2021 also built the ML model year-by-year, starting from 2013). The large sample size aids the building of a more robust model. (3) We introduce more derived meteorological variables than most studies by feature engineering.

Therefore, to make a fair comparison of the model per se, we use six popular ML/DL models, with the same periods, stations, and input parameters as the deepWIA model, including two RF, two XGB, and two MLP models using the input data over 3 d (i.e., the same as the deepWIA) and only 1 d that is fitted, named RF1, RF3, XGB1, XGB3, MLP1, and MLP3 respectively (Table 3). The MLP models have nine full connection layers with the maximal 512 neurons in the fifth layer. Following the previous studies, all the models fit the PM2.5 concentrations directly. It should be noted that these models are applied here for the role of meteorological variables and thereby do not introduce satellite or visibility data, so the RMSEs here are slightly higher than those reported in previous studies.

These six models all have higher RMSEs and lower R2 than the deepWIA model in the test set (even than that of the AbExp_1, which also fits PM2.5 concentrations directly; Fig. 8a). The models with 3 d data always performed better than these with only 1 d data, indicating the importance of temporal information. Additionally, there is more severe overfitting for these models than the deepWIA model, as evidenced by the large performance difference between the training and test sets, especially those of the RF1 and RF3.

The advantages of deepWIA over traditional RF, XGB and MLP models should be attributed to two points: (1) the deepWIA model is much deeper than the commonly used RF, XGB and MLP models, which aids learning of the complex nonlinear relationship between meteorology and aerosol concentration; and (2) previous models do not necessarily include temporal correlations of aerosol concentrations; rather, some use a predefined spatiotemporal distance for the injection of temporal information (Wei et al., 2019a, b, 2020; Li et al., 2020). The deepWIA model uses gate parameters to learn dynamic links of aerosol concentration among days.

We also compare the deepWIA and two semiempirical meteorological indices for aerosol pollution, namely PLAM and ASI. These indices are commonly used to assess meteorological effects on variations in aerosol concentrations (Wang et al., 2021; X. Zhang et al., 2019). PLAM was applied to the NCP (Yang et al., 2016), using visibility as the target variable, while ASI was applied to North and Northeast China, using PM2.5 concentrations as the target variable. Both indices only considered the meteorology on that day only. By comparison, as described in Section 2.1, deepWIA includes all the kernel variables of these two indices, as well as other spatiotemporal information. It will form the best DL model to take advantage of these variables. Hence, its applicability extends to the whole country. Additionally, PLAM and ASI cannot provide a uniform model for PM2.5 concentrations, unlike deepWIA. PLAM focused on the relationship between meteorology and visibility; ASI just illustrates the temporal relationship between meteorology and PM2.5 concentrations, which varies from location to location. Therefore, estimating PM2.5 concentrations also requires additional linear modeling at each grid cell. Due to these advantages, the deepWIA could be a better tool for assessing the impact of weather on aerosol concentrations.