The dust storm event studied in this paper took place in East Asia in April 2015, and has already been used as a test case for assimilation experiments in . The LOTOS-EUROS/dust simulation model is used with configurations similar to those in our previous studies, which were configured on a domain from 15 to 50∘ N and 70 to 140∘ E, but with a higher model resolution of 0.25∘. The model is driven by European Centre for Medium-Range Weather Forecasts (ECMWF) operational forecasts for horizons of 3–12 h. The dust load is described by five aerosol bins within a diameter range of 0.01 µm <Dp< 10 µm. Physical processes included are emission, advection, diffusion, dry and wet deposition, and sedimentation. The dust emission scheme implemented in LOTOS-EUROS is mainly based on the formulation of horizontal saltation flux and sandblasting efficiency . A terrain preference parameter Fps was used in the dust emission in . This geographic-dependent parameter was first introduced by , and used to approximate the probability of having accumulated sediments that can be resuspended. In this work, Fps is disabled since the preference factor was found to limit the emission rate in some regions where the fine-scale topographic feature is actually unknown. Snapshots of a reference simulation of the dust episode have been taken and are shown in Fig. a.

The China Ministry of Environmental Protection (MEP) has commenced to release the hourly-average measurements of atmospheric constituents including PM2.5, PM10, CO, O3, NO2, and SO2 since 2013. A huge number of ground stations measuring these air quality indices have been established in densely populated areas. At the present, the monitoring network has grown to 1500 field stations covering all of China as shown in Fig. .

The assimilation system, which will be used to combine bias-corrected PM10 observations with simulations, is based on a reduced-tangent-linearization four-dimensional variational (4D-Var) data assimilation. The goal of a 4D-Var technique is to find the maximum likelihood estimation of a state vector, which is here the dust emission field f, given the available observations over a time window. A common approach is to use an incremental formulation, which aims to find the optimal emission deviation δf as the minimum of the cost function: 2J(δf)=12δfB-1δf+12∑i=1kHiMiδf+diTRi-1HiMiδf+di, where k is the number of time steps within the assimilation window. The vector δf denotes a perturbation of the emissions with respect to the background one. For an observation time i, the innovation vector (length mi) is defined as the difference between the simulations and observations: 3di=Hi(Mi(f))-yi, where Mi denotes the LOTOS-EUROS/dust transport model, Hi is the operator that converts state variables into observation space, and yi is the vector with dust observations at this time step i. The operators Hi and Mi denote linearizations of Hi and Mi around the reference emission vector fb. Following , the errors in dust emission field were assumed to be only caused by the uncertainty in the friction velocity threshold in the dust windblown parametrization, and similar assumptions on the uncertainty are used to build an emission error covariance B. The friction velocity threshold is perturbed with a spatially varying multiplicative factor β. β is configured with a mean of 1 and a standard deviation of 0.1. In addition, an exponential profile of distance-based spatial correlation is posed on β values . The observation error term is weighted by an observation error covariance R, for which the individual elements will be described in Sect. 4.1.

To reduce the computational cost in calculating the tangent linear model Mi, a reduced-tangent-linearized 4D-Var is used. The simplified method is based on proper orthogonal decomposition (POD) of the background covariance B, which efficiently carries out model reduction by identifying the few most energetic modes: 4B=UUT≈ŨŨTδf≈Ũδw, where U∈RP×P is the background emission covariance square root, with P the size of the emission field of O(104) elements, while Ũ∈RP×p is the truncation of U based on POD, with p the reduced rank size of O(102). The vector δw∈Rp stores the transformed control variables.

The cost function of the reduced-tangent-linearization 4D-Var is formulated as 5J(δw)=12δwTδw+12∑i=1kHiM̃iŨδw+diTRi-1HiM̃iŨδw+di, where M̃i denotes the reduced tangent linear model with a rank p, which is approximated using the perturbation method. More details about the reduced-tangent-linearization 4D-Var algorithm can be found in .

In real applications, the observations inevitably have biases which cannot be attributed to the model simulation, as follows: 6yi=Hi(Mi(f))+bi+σi, where σi is the vector of Gaussian-distributed observation errors which have zero means and a known covariance matrix Ri, and bi denotes the vector of observation bias. In our application, the vector yi contains the observed PM10 concentrations, while the aerosols released in the local anthropogenic activities and other non-dust-related processes are referred to as bi. Note that the PM10 measurements themselves might also contain “native” biases due to incorrect sensor reading or systematic errors. However, this part of the bias in the PM10 observations is unknown and not considered in this study.

In the course of data assimilation, it is impossible to determine whether the departures (di) of the prior simulations from the observations are due to the biased observations bi or emission errors δf. Thus, the assimilation result will diverge from the true state when a bias is present. In complex dynamic models such as the atmospheric transport model, the biases (non-dust aerosols) could have high spatial and temporal variabilities and are therefore difficult to quantify.

In this work, we proposed two methods to quantify the bias levels for the observation bias correction. The first one is the non-dust parts of the LOTOS-EUROS chemistry transport model (CTM) which simulates the aerosol life cycles including emission, transport, and deposition. The second method is to describe the non-dust aerosol levels using a data-driven machine-learning model. Details of these two methods are illustrated in Sect. 3.

In fact, both LOTOS-EUROS CTM and the machine-learning model are imperfect, and some biases might still exist after the correction. The former is known to be limited by errors in the emission inventories, meteorological forecasts, and all kinds of input sources. The latter is then hampered by the deficiency of the type model (e.g., insufficient to represent the complexity of the phenomenon) and an inadequate amount of training data. However, by combining the bias-corrected observation with the dust model, the assimilation will adapt to a posteriori values which are more close to reality.

There were a few studies that addressed both the model deficiency and uncertainty in observation bias simultaneously using either variational data assimilation or sequential filters . Those assimilation schemes not only require a formulation of a model for the bias, but also need a quality-assured reference to describe the uncertainty of the bias model. The need to attribute errors to their proper sources is obviously a key part in any assimilation system but becomes especially critical when it involves bias correction. This is because a wrong error attribution will force the assimilation to be consistent with a biased source. If the source of a known bias is uncertain, assimilation without considering the uncertainty of the bias model is the safest option . Therefore, these two non-dust models are solely set as references for the bias, and the uncertainties are not explored here.

Figure  shows a timeline for the assimilation experiment around the April 2015 dust event, which is very similar to what was used in . The dust event has a short duration, and therefore only a single assimilation window with a length of 36 h is used. The dust emissions take place at the start of the window, while the observations become available at the end of the window since they are located downwind from the source region (see Fig. ). A long assimilation window is therefore necessary in order to estimate the correct emission parameters given the observations.

When we perform the assimilation analysis on 15 April, 19:00 China standard time (for all times throughout the paper), only the dust observations from 15 April, 08:00 to 19:00, will be assimilated and they are calculated by subtracting the non-dust part (CTM based or ML based) from the PM10 observations. After the analysis, the simulation model is used to perform a dust forecast for the next 12 h using the newly estimated emission parameters. A fully aerosol PM10 forecast will then be calculated by adding the dust forecast and non-dust aerosol forecast, where the latter again originates from either the CTM or the machine-learning model.

The regional CTM LOTOS-EUROS/non-dust is configured similar to LOTOS-EUROS/dust used in the assimilation, but now includes all trace gases and non-dust aerosols. The configuration is similar to what is used for daily air quality simulations over China as described in . Anthropogenic emissions are taken from the Multi-resolution Emission Inventory for China (MEIC) (http://www.meicmodel.org, last access: 1 July 2019). Natural emissions included are the sea salts that are calculated online, biogenic emissions that are calculated online using MEGAN , and wildfires which were taken from the operational GRAS product . The LOTOS-EUROS full aerosol operational forecast over this modeling domain is released via the MarcoPolo–Panda projects (http://www.marcopolo-panda.eu/, last access: 1 July 2019).

The operational CTM LOTOS-EUROS over China is in its early phase of development as well as the other six CTMs used in the MarcoPolo–Panda projects. The purpose of these projects is to diagnose statistical differences between the ensemble model simulations and observations. An important objective is to determine ways by which the models can be improved. These differences are mostly attributed to inaccuracy in the weather forecast and errors in the adopted surface emissions . Indeed, there is room for minimizing the forecast–observation differences using nudging methods like data assimilation, which requires considerable efforts and is not yet exploited in that study.

Given a set of training data, a machine-learning algorithm attempts to find the relation between input and output. When a proper model is used, the machine-learning algorithm can learn to reproduce the complex behaviors of a dynamic system. The description is purely based on the data; physical knowledge is not included. Machine-learning algorithms are popular tools to forecast air quality indices using historical records . In this study, the machine-learning algorithm used is the long short-term memory (LSTM) neural network, which has demonstrated its ability in predicting time series problems .

The LSTM operator L, which is configured with parameters θ, for predicting non-dust PM10 can be described as 7bt0+t=Lθ(xt0,xt0-1,…,xt0-m+1), where bt0+t represents the predictor, which is in this study the non-dust PM10 concentration forecast t hours in advance. The temporal correlation between the input and output features declines when t increases. In our system, the maximum forecast period t is 12 h. The input vectors xt0,xt0-1,…,xt0-m+1 are the observed data of the past m hours, which is set as 18 h empirically. The input vectors consist of

hourly observations of PM2.5, SO2, NO2, O3, and CO from the ground-based air quality network described in Sect. ;

Dust storms themselves occur with very low frequency. To our knowledge, the studied dust event is the most severe one since 2002, and there are no such large-scale dust events recorded in our training period. Note that cities that are close to the Gobi and Mongolia deserts might have experienced several small-scale dust events with a limited increase in dust concentrations. However, the machine learning tries to find the global best fits for the whole training dataset. The default learning rate, which determines the weights are updated during training, on a simple sample is 10-4 in our machine-learning algorithm. Therefore, the PM10 records yb are very close to the non-dust PM10 concentrations, and the rare dust event records are not excluded from the training dataset for convenience and for the expected little impact on the training result. The regression model L is thus assumed to reflect only the relation between input features and the non-dust PM10.

Note that including PM10 observations in the series of input vectors will certainly improve the skill of the machine-learning forecasts. However, the LSTM model would then lack the ability to discriminate between the dust and non-dust fractions in PM10 during a dust event. Earlier studies showed that the input variables, including PM2.5, are independent of the dust storm as illustrated in .

For the non-dust PM10 machine-learning forecasts in a given site, observations from its nearby sites are also vital and are used in two ways. First, missing data records are unavoidable in an air quality monitoring network, while the LSTM model training requires an uninterrupted time series of features. In this study, data interpolations of air quality measurements (PM10, PM2.5, SO2, NO2, O3, and CO) are performed using both a linear interpolation and a k-nearest-neighbor algorithm if a site has no more than 30 % of missing data. Otherwise, all the measurements at the given sites are abandoned. Generally, more information available from the nearby sites will result in a more accurate interpolation. Second, learning in the presence of data errors is pervasive in machine learning, and the measurements from nearby stations are used to limit their influence. Data errors occur due to incorrect sensor readings, software bugs in the data processing pipeline, or even inaccurate data interpolation. Statistical analysis tests have been conducted which did not only indicate a strong correlation between the non-dust PM10 and air quality measurements at the given sites, but also show that the predictor (non-dust PM10) is correlated with the observation indices (especially the PM2.5) at its nearby sites. In order to eliminate errors caused by incorrect inputs at the modeling site, the measurements at the nearby stations are considered to be the essential indices. In this study, a data instance will only be selected for training the LSTM model if there is at least one nearby site within an empirical radius 0.8∘ (approx. 80 km), and a maximum of three nearby sites will be randomly selected where observation stations are densely distributed. To save the computation costs on machine-learning model training, only PM2.5 from nearby sites is included as input in this study.

The machine-learning model for non-dust PM10 forecast is trained site by site, with the hyper-parameters shown in Table . With the following hyper-parameters, the machine-learning model training takes several minutes for each site. The training at each site is independent; hence, the whole workload is highly parallelizable.

Figure  presents the original field observation network (N≈1500) established by the China Ministry of Environmental Protection (MEP) up to 2018, as well as the sites (N=1351) where LSTM-based non-dust forecasts are performed. It is clear that the LSTM forecast cannot be performed at each monitoring site. A few of the sites are skipped due to the lack of nearby sites; the rest are skipped because of a high data missing rate in the training period.

Our two bias models, LOTOS-EUROS/non-dust and LSTM, could both be used for air quality forecast operationally when there is no dust storm. Once a dust storm is observed, the dust emission inversion system will be enabled, and the two non-dust PM10 models will then be used in dust observation bias correction. The forecasts are expected to have a good performance when dust is not present and to underestimate the PM10 levels in the case of dust storms.

Both CTM LOTOS-EUROS and LSTM are tested to forecast non-dust PM10 over April–May 2015. This period includes the 2–3-day dust event that is used as a test case for the assimilation. Figure a–c show density plots comparing PM10 observations with either LOTOS-EUROS/non-dust forecasts or LSTM forecast 0 and 12 h in advance.

The CTM LOTOS-EUROS/non-dust in general underestimates the non-dust PM10. The forecast results in a relatively large root-mean-square error (RMSE) of 89.4 µg m-3. This could be explained by the fact that not all types of particulate matters, such as secondary organic aerosols, are included in the model, and some aerosol emissions are very difficult to estimate (e.g., wood burning by households). The two LSTM forecasts show on average a good agreement with the observations. The RMSEs of the forecasts by the two machine-learning models in the 2 years of the training period are reduced to 55.9 and 60.7 µg m-3, and in the 2-month test period (excluding the dust event from 14 to 16 April) they also stay at comparable low levels of 58.6 and 60.2 µg m-3. As expected, a smaller forecast period t=0 h gives a better result than the forecast over 12 h.

The scatters in the dust period (14–16 April) are denoted using different markers in Fig. . The underestimation of PM10 during the dust period (14–16 April) is visible in the bottom right corners of these plots.

When we perform the assimilation analysis on 15 April, 19:00, the short period of t=0 h forecast will be treated as the non-dust levels in the bias correction of the original PM10 measurements. Note that here t=0 forecasts denote the forecasts are valid at each specific snapshot of the observations, while the 12 h forecasts are valid 12 h in advance; e.g., the non-dust PM10 forecast (12 h) on 16 April at 07:00 is valid on 15 April at 19:00. Subsequently, the bias-corrected data are used to estimate the dust emissions over the past 36 h window. Obviously, one important aim of the assimilation is to make a better forecast, in this study, the forecast skills will be evaluated in the following 12 h from 15 April, 19:00. In addition, the forecast is assessed by comparing the combined PM10 forecasts to PM10 observations. The LSTM forecast with t=12 h in advance will be added to the dust storm forecast to build the combined aerosol forecast.

A key element of the data assimilation system is the observation error covariance matrix R. This covariance quantifies the possible difference between simulations and observations. The observations with a smaller error have a higher weight in the assimilation process.

In related works, the dust observation errors were usually empirically quantified. assumed that the observation error is proportional to the measurement with a constant factor of 10 %. used a similar error setting but also assigned a larger error to low-value measurements since the model might easily result in relatively large errors when simulating minor dust loads.

Theoretically, the observation uncertainties are due to the representation errors as well as the measurement errors, while the former is widely considered the largest source. Limited by the computation resources, our dust model uses a spatial resolution of 25 km, while the in situ measurements cover much less of the atmosphere surrounding them . This of course limits our capability of resolving the fine-scale fields that are reflected in observation spaces. Therefore, the spatial representation error is assumed to be the dominant error source and taken into the account in approximating the observation uncertainties. In addition, the error due to the different bias correction terms is indeed another source. It is not yet considered in this study but will be exploited for a more accurate assimilation operation in our future work.

The spatial representation error quantification itself is a complex task. It could be calculated through comparing the model simulations at different scales of resolutions. In this study, the availability of multiple measurement sites in a single model grid cell provides an alternative way to quantify the representation error. When multiple observations are present, the statistical error in the observed values reflects the spatial representation uncertainty. An example is the grid cell covering the city of Beijing, where observations from 12 different field stations are available. Note that it is the grid cell which has the most monitoring stations. The spread of the hourly measurements is shown in Fig. c. For each hour, the standard deviation of the measured PM10 values is plotted against the mean in Fig. , where the red markers represent “regular” polluted conditions, and the blue markers the dust event. The result shows that the spread in the observations closely agrees with the average pollution level during the dust event. Based on this result, a simple linear regression is used to obtain a parametrization for the observation representation error: 9σ=max⁡(a⋅y+b,σmin)[µgm-3], where a=0.12 and b=55.7 are the linear regression parameters based on the dust event data (blue markers). It should be noted that the observation sites in Beijing truncate observations at a maximum of 1000 µg m-3, and therefore observations close to this number are not used since the true values might have been much higher. A minimum observation representation uncertainty of σmin=100 µg m-3 is used for the dust observations (PM10 with bias correction) to avoid a too strong impact of low-value observations (hardly dust) on the estimation of dust emissions. In case the simulation model estimates dust concentrations at the surface while in reality the plume is elevated, the low-value observations might lead to an unrealistically strong decrease in the dust emissions.

The representation uncertainty has already been validated to fluctuate in space . However, for most other grid cells the number of observation sites is simply one, which makes it difficult to parametrize a representation error in a similar way. Therefore, the representation error parametrized for Beijing is used for all other locations too.

Note that the raw PM10 and the bias-corrected dust measurements might have different uncertainties in representing the real dust storm level. This is not yet taken into account in our study, and the three types of the assimilated measurements, raw PM10 and bias-corrected dust observation using either a CTM or machine learning, are all configured with the same observation error in Eq. (). In addition, all the measurements are assumed to be independent; hence, the observation error covariance R is diagonal.

To evaluate the a posteriori dust emission field that is obtained by assimilation of the bias-corrected dust observations, an emission index Fi (g m-2) is defined as in . The index represents the accumulated dust emission in a cell i between 14 April 08:00 and 15 April 19:00. Figure  shows the emission index map of the a priori model and a posteriori emissions obtained from assimilation of either the original PM10 observations, or the LOTOS-EUROS- or LSTM-based bias-corrected dust measurements.

As shown in Fig. a, the a priori emission was in general rather weak, which resulted in an underestimated surface dust concentration simulation as can be seen for example in Fig. a.1–a.2. The a posteriori emissions are almost everywhere higher than the a priori. An exception is the region marked in black, where the a priori emissions are higher. The emissions from this black-dashed region contributed to a too-early arrival of the dust peak in the model cells over Hohhot and Xingtai as shown in Fig. a and c.

Figure b shows the emission index F that results from directly assimilating the original PM10 measurements. As expected the estimated emissions are higher than those obtained by assimilating the bias-corrected observations since all airborne aerosols observed are considered to be dust. In comparison, the assimilation with the LSTM baseline removed data results at a modest emission level as shown in Fig. d. The emissions estimated with LOTOS-EUROS-based bias-corrected observations are in between since the resulting dust observations also overestimate the actual dust loads compared to the LSTM-based bias-corrected dust measurements.

Figure a–d show the dust simulations at the surface layer at the end of the assimilation window (15 April, 19:00, left column) and the forecast 3 h later (22:00, right column) using the newly estimated emission field. Note that the average dust concentration over the affected downwind regions reached a peak around 22:00. Compared to background simulations in , the a priori model simulations have been improved by disabling the topography-based preference factor as mentioned in Sect. ; however, a large difference from the bias-corrected PM10 observations in Fig. e is still present.

The a posteriori concentrations in Fig. b.1–b.2 are the result of assimilating the original PM10 observations shown in Fig. a.1–a.2. As expected, these lead to the highest simulated dust concentrations since all the aerosols observed are assumed to represent dust. Especially in the center of the plume, the dust concentration can be as large as 2000 µg m-3. Figure c.1–c.2 show the results when using the LOTOS-EUROS/non-dust bias-corrected PM10 observations as dust, and although concentrations are lower, they are still likely to overestimate the real dust levels. The a posteriori results using the LSTM bias-corrected measurements provide the lowest dust concentrations as shown in Fig. d. Only in the grid cells that are close to the source region, do the surface dust concentration reach values as large as 2000 µg m-3, while in the downwind areas the maximum dust concentrations are usually below 1200 µg m-3.

To illustrate the improvements of assimilating bias-corrected measurements, Fig.  shows the observed and simulated PM10 concentrations in the aforementioned grid cells covering Hohhot, Beijing, and Xingtai. These locations are neither the best nor the worst examples, but illustrate typical results and challenges to be solved in future. For a fair comparison with the PM10 observations, the non-dust aerosol concentrations obtained from either LOTOS-EUROS/non-dust or LSTM were added to the dust simulations from the inversion system.

The site Hohhot is close to the main dust source region. The a priori model simulated the arrival of the dust plume 8 h before it was actually visible in the PM10 observations. The assimilation of the observations is able to produce simulations in which the dust plume arrives at the correct time. The assimilation with LSTM bias-corrected data has the best performance, with the peak of the simulated concentrations (dust plus bias) most close to the observed PM10. During the forecast period (t> 15 April, 19:00), all three assimilation-based forecasts show a decline in concentrations, which slightly overestimate the observations. This can be explained from the fact that the dust storm is a strong flow-dependent phenomenon in which concentrations at a certain location are strongly correlated to earlier concentrations at upwind locations. For Hohhot, only a limited number of observation sites are located upwind, and therefore hardly any data are available to constrain the concentrations at this location. To improve the forecast at Hohhot it will be necessary to have additional observation data, for example from sites actually within the source region, or from satellites observing the aerosol load over the source region .

For the grid cell Beijing, which is located further downwind from the dust source region, the arrival of the dust peak is correctly simulated. However, the amplitude of the concentration peak is underestimated compared to the average PM10 observations. As can be seen in Fig. , the dust plume forms a rather small band over central and northeast China. In each of the three assimilations, the dust concentrations in the band are rather low around Beijing. This suggests that the simulation model simply is not able to increase the dust concentrations here, for example because of uncertainties in the meteorological data, a removal of dust that is too efficient, or because some local sources of dust are absent (equally, non-dust PM10 levels are underestimated).

The grid cell Xingtai is located more to the south, and the model is able to simulate high dust concentrations here. The a priori model simulates the arrival of a first dust peak already at 13:00, which is however not visible in the PM10 data. The assimilation postpones the arrival of the main dust, which according to the measurements takes place around 22:00 and is already in the forecast period. The forecast simulations all overestimate the amplitude of the peak, especially when using the original PM10 data as proxy for dust. The assimilation with the LSTM-based baseline removal shows the best agreement with the observations.

To evaluate the forecast skill of the assimilation(s), the root-mean-square error (RMSE) of the reference and three a posteriori fully aerosol simulations (dust forecasts plus non-dust predictions) with respect to the observed PM10 over the whole observation sites has been computed for each hour. A time series of this RMSE is shown in Fig. ; after the assimilation window (marked period), the results are based on the forecast simulations. The a priori RMSE values at the end of the assimilation window and during the forecast are about 200–250 µg m-3. Direct assimilation of the original PM10 measurement actually increases these values to above 300 µg m-3 during the forecast since dust concentrations become strongly overestimated. Assimilation of the LOTOS-EUROS/non-dust baseline-removed observations nonetheless reduces the RMSE, in particular within the assimilation window. The strongest decrease in RMSE is obtained using the LSTM-based baseline removal, with values of 120–200 µg m-3 during the forecast.

Both our CTM and machine-learning-based bias correction methods have room for improvements. It might be useful to improve the CTM simulations by assimilating PM10 observations during the hours where no dust storms are present and use these improved simulations to remove the non-dust part of the observations during an event. These additional assimilations would then involve repeated forward ensemble bias–model runs which could be computationally expensive. The machine-learning model in our non-dust PM10 simulation can also be further optimized, such as using a different configuration or deeper neural network, including extra input features like non-dust PM10 simulation from CTMs and other related records.

We will exploit the variabilities of the representation errors comparing the model simulations at different spatial resolutions. The error from the bias correction term will also be taken into account while calculating the observation error.