Emissions inventories of black carbon (BC), which are traditionally
constructed using a

Black carbon (BC) refers to light-absorbing carbon aerosols produced by all kinds of incomplete combustion processes (Bond and Bergstrom, 2006). It is an important component of atmospheric particulate matter, affecting weather, climate and air quality, and therefore attracts much attention among the scientific community. Its absorptive nature, which directly causes reductions in incoming shortwave solar radiation, is a key contributor to climate forcing by aerosols (Liousse et al., 1993; Menon et al., 2002; Hansen et al., 2005; Ramanathan and Carmichael, 2008). BC aerosols have been shown to act as cloud condensation nuclei when they become hydrophilic, affecting cloud microphysical properties and rainfall processes (Lary et al., 1997; Bond et al., 2013). The lifetime of BC is about 3–10 days, and it can be transported far from its source to affect remote and pristine areas (Hansen et al., 1988; Hara et al., 2008). Its light-absorbing properties reduce atmospheric visibility (Wolff, 1981). Qiu and Yang (2000) showed that BC contributes to the considerable degradation in optical depths and visibility noted in northern China. Furthermore, from the human health perspective, these particles, which are generally sub-micron in size, contribute greatly to the threat of pulmonary diseases, as they can penetrate into the lungs while also carrying a variety of toxic elements with them. Therefore, an accurate picture of the distribution and variation of BC is crucial to our understanding of climate change and pollutant dynamics, and ultimately helps us to develop better policies to tackle associated environmental problems.

However, there is considerable uncertainty involved in the estimation of the
distribution of BC and its contribution to BC emissions inventory, which is
traditionally constructed from the

Inverse modeling is a powerful approach to observation-based inferences about
atmospheric model inputs (e.g., emissions). Hakami et al. (2005) developed a
4DVar inverse modeling method for the recovery of BC emissions, and sizable
improvements were found at sub-regional levels. However, the domain-wide
emissions inventory did not change significantly because measurements at only
four observation sites were used to inverse and assimilate. Employing a
multiple linear regression model, Fu et al. (2012) derived a

The ensemble Kalman filter (EnKF), introduced by Evensen (1994), a technology based on ensemble forecasting and Kalman filter theory, has been successfully employed in atmospheric chemistry analyses, such as dust storm and aerosol data assimilation (Lin et al., 2008; Sekiyama et al., 2010; Tang et al., 2013). EnKF has some advantages over 4DVar insofar as it does not require the reconstruction of an adjoint model, which is technically difficult and cumbersome for the complex chemical transport model. However, the algorithm is highly sensitive to ensemble size (Mitchell and Houtekamer, 2002), and therefore tends to be computationally demanding and has limited use in large-scale and online atmospheric chemical transport models. Moreover, the EnKF method assumes that the probability density functions (PDFs) of the initial conditions, emissions and observations are Gaussian in their distributions. When there is large bias, problems such as filter divergence will lead to analysis failure.

In this paper, an ensemble optimal interpolation (EnOI) data assimilation method is used to investigate the possibility of optimally correcting the spatially resolved emissions bias of BC. The background-error covariances are estimated using the ensemble, but the model only needs a single forecast, allowing for the use of a larger ensemble than EnKF. The preliminary results for the inverse emissions for BC are presented in this paper. The details of the methodology are described in Sect. 2, followed by a description of the model and the observations used in Sect. 3. The inverse modeling results are presented in Sect. 4, and a summary and discussion is provided in Sect. 5.

Air quality models can be generally written as

The observations are assumed to be also available at time

Without observations, we can carry out a simulation with a given initial
concentration, emission inventory, and ignore model error to solve Eq. (1) and
to obtain a numerical solution

Zhu and Wang (2006) introduced the formulation of this estimation theory
given the PDFs of the initial condition, emissions and observations are
Gaussian distributed. The inverse method seeks an optimal estimate of the
emission that is consistent with both the observation and
prior
constraints of source by minimizing the following cost
function:

Based on the Kalman filter, we have the following analysis equations to
minimizing the cost function:

To solve Eq. (4), we can use the ensemble method. First, we generate the

The analysis includes updating each

Then, the estimated emission is

The EnOI analysis is computed by solving an equation similar to Eq. (4), written
as

The GRAPES–CUACE model domain and BC observation sites used in this study. Observations considered for assimilation are shown as red points, while observations considered for verification are shown as blue stars. Information about stations is shown in Table 1.

The model used in this study is an online-coupled chemical weather forecasting system, Global/Regional Assimilation and Prediction System–Chinese Unified Atmospheric Chemistry Environment model (GRAPES–CUACE), which consists of two components: (1) GRAPES is a mesoscale meteorological model developed by the China Meteorological Administration (CMA). It produces meteorological fields (winds, turbulence, precipitation, etc.) to drive the CUACE chemistry model. (2) CUACE includes emissions, transport, dry and wet depositions, and removal both in and below clouds of both gases and aerosols (Gong and Zhang, 2008; Wang et al., 2009; Zhou et al., 2012). These two parts are coupled online. Using the national official basic information of emission sources published in 2005 based on the bottom-up inventory developed by Cao et al. (2006), the emission subsystem (EMIS) provides hourly gridded offline emission intensities of 32 species, including seven categories of aerosol species (sea salt, sand/dust, BC, OC, sulfates, nitrates and ammonium salts) in the aerosol modules over the model domain. The basic gridded BC emissions inventory is based on energy consumption and activity information for various emission sectors: industry, residential, transport, power generation, agriculture, biomass burning and others.

The model domain for this study is approximately (70–140

Observation site information.

Emission ensembles at grid (116.5

The ensembles of BC model simulation at grid 116.5

BC emissions inversed by observations from site Zhengzhou (ZZ):

The near-real-time (NRT) data used in this work are the surface daily and hourly BC concentrations collected from over 30 CMA Atmosphere Watch Network (CAWNET) stations. The locations of these sites are shown in Fig. 1. Observations considered for assimilation are shown as red circles, and observations considered for verification are shown as blue stars. Information on the stations is presented in Table 1. The rural stations are typically located some 100 km away from local pollutant sources or nearby major cities, and at moderate height above the area's local elevation. At the urban stations, the sampling heights are 50–100 m higher than the ground level. This enables the production of samples that are representative of the region, rather than the immediate locality.

The BC observations are obtained using Aethalometer (Model AE-31, Magee Scientific, Berkeley, California, USA) instruments, which measure optically absorbing filterable aerosol material at a 5 min time interval (Zhang et al., 2008) at seven wavelengths of 370, 470, 520, 590, 660, 880 and 950 nm. The BC concentrations used in this study are derived from the optical absorption at 880 nm.

We conduct 1-year-long simulation using bottom-up emission for 2008. NCEP
1

BC monthly mean concentrations (units:

A good ensemble system should satisfy at least two conditions: (1) the
ensemble mean should be close to the truth; (2) the ensemble spread should be
a reasonable representation of the root mean square error (RMSE) between the
ensemble and the truth. Because the atmospheric components are usually
log-normal distributed, we produced N ensembles of the emissions according
to the formula below:

BC emissions from China inversed by 27 observation sites (units:

The inverse modeling of the BC emissions in this study uses the ensemble member to calculate the background-error covariance matrix between the concentrations and emissions. The accuracy of the matrix is a very important factor for the inverse result. Since we cannot obtain as many ensembles as model dimensions, we should employ appropriate techniques that eliminate the effects of sample error and that localize the impact of an observation to a subset of the model state variables. Figure 4a shows the correlation of the background-error between the sites concentrations and emissions. The figure shows that the site concentration is highly correlated with the emissions near the site, which is expected. However, there are some emissions from remote regions that are also correlated with the site concentration, i.e., spurious correlations. Localization is an essential tool for an ensemble-based assimilation to adequately span the model sub-space.

Usually, a typical implementation of localization involves the
multiplication of the ensemble-based covariance by a correlation function,
so the gain matrix is re-expressed as Eq. (12). We use the distance–dependent
covariance localization scheme,

Here, we use an elliptic function with

Figure 4c shows the correlation of the background error between the site concentrations and emissions. Using this localization scheme, the spurious correlations far away from the site concentration are reduced, but the pattern of correlation around the site remains. Therefore, the inversion provides a more accurate estimation of emissions.

BC daily concentrations in January 2008 (units:

Estimates of provincial BC emission (Gg) by bottom-up and inverse method.

An 1-year-long simulation is conducted, driven by the current Chinese
bottom-up emissions inventories for BC, and the results are compared with
surface-observed BC concentrations (Fig. 5). The comparison of model results
to observations evaluates the bottom-up inventories. Figure 5a compares the
seasonal variation of observed and simulated surface BC. The simulated
concentrations are significantly lower than the observed throughout the
year. This indicates a region-wide underestimation in monthly and annual
bottom-up emission inventory. The average simulated annual mean BC
concentration is 1.19

Model simulations and surface observations of monthly mean BC
concentrations at assimilation sites and verification sites (units:

We use the 27 BC monthly observations to inverse the emissions. Figure 6 shows the bottom-up or prior emissions (E1) and inverse emissions (E2) for January and July. There are significant increases in the E2 emissions over most regions of China, including eastern China, central China, Sichuan basin and western China. Only the regions around Beijing and the northeast part of Heibei province present a bit of a decrease in E2, because model simulation at the assimilated site SDz is lower than the observation. The results show that the basic emissions produced by the bottom-up method are underestimated and have been corrected by EnOI in most regions of China in January, not only in eastern China and central China where the rural population density and economic level are high, but also in northwestern China, which has a lower rural population densities and lower economic level.

Table 2 compares our inverse provincial and national emission of BC with bottom-up inventories. The five largest contributions by province in E1 for January are from Hebei, Shangdong, Henan, Shanxi and Sichuan. In E2 by the inversion, the five largest BC emission province are same with E1, but emissions are greatly enhanced in many provinces. We find emission from half of the provinces in China to be enhanced by a factor of over 2 for January. The resulting estimate emission over China in January and July is 240.1 and 169.5 Gg, respectively. Figure 9 shows the seasonality of BC emission in China. The emissions in every month were enhanced after the inversion. The annual emission of bottom-up inventory is about 1449.6 Gg, and inverse inventory is about 2539.3 Gg.

The root mean square error (RMSE) between the daily model simulation
and observation. The blue bars show the RMSE between the daily model
simulation driven by prior emissions (E1) and observations, and the red bars
show the RMSE between the daily model simulation driven by inverse
emissions (E2) and observations (units:

Seasonality of BC emission in China (units: Gg).

While inverse modeling can provide a simplified solution, the processes contributing to the model bias and error go beyond emission. Therefore, emission inversion is likely to lump up uncertainties from other processes into emission. Although we had used monthly mean concentration to eliminate the effect, it is still important to evaluate the inverse emission estimation and uncertainty of the result. Table 3 lists the monthly mean BC concentrations at the observation sites. It shows that there are large errors between the monthly BC concentration simulations driven by the bottom-up emissions (E1) and observations. Most of them feature a negative bias. After EnOI inversion, the model simulation for most observation sites in China is much closer to the observation, even for the verification sites. The error percentage decreases from 78.97 to 39.54 %, which is an almost 50 % decrease.

Figure 7 shows the variations in daily BC concentrations in January 2008. The red line shows the observations, the blue line is the model simulation driven by prior emissions (E1), and the green line is the model simulation driven by inverse emissions (E2). Even though we only employ the monthly mean BC measurements to inverse the emissions, the accuracy of the daily model simulation is also improved. Take the Zhengzhou site (ZZ) for example, driven by inverse emission inventory, the daily simulation concentration and its variation are more consistent with observation. Observations in the ZZ site exhibit a peak during 2–8 January the simulation with E1 does not present, whereas the simulation with E2 does. We calculate the RMSE between the daily model simulation and observation (Fig. 8). The blue bar is the RMSE between the daily model simulation driven by prior emissions (E1) and the observation, and the red bar is the RMSE between the daily model simulation driven by the inverse emissions (E2) and the observation. As we can see, almost all of the RMSEs decrease, with the average RMSE dropping from 5.08 to 3.47, which is a decrease of about 31.56 %. Because there are large region-wide underestimations in the bottom-up emission, not only in the densely populated and industrialized areas such as northern China, the Yangtze River Delta and the Sichuan basin, but also in northwest China, which has a lower population densities and lower economic level, the model performance of daily BC concentration is very poor. The simulation at rural and urban sites are significantly lower than the observations. With inversion by EnOI, the emission negative bias has been corrected, the simulated concentrations increase and improve. However, there are still large difference between the daily observations and simulation, because there are some other sources of uncertainty such as meteorology and other factors of model error. We have used monthly mean data in the inversion process to reduce these effects, but when it comes to hourly and daily simulation, these effects should be considered reasonably, which is part of the future work we have planned.

Uncertainty analysis for annual Chinese BC bottom-up and inverse emission inventory.

From the figures and tables above, it is apparent that the biases of the BC emission intensities in China at each grid point are corrected by the EnOI inversion system. Where the bias is large, the RMSE decreases significantly. However, if there is small bias, such as in the ZhuZhang site, the correction is tiny, and the RMSE changes very slightly. We also find that, near Beijing, emissions around the SDz site are overestimated because the observation in that site is lower than the simulation. However, after the inversion, the BC concentration at the verification site Beijing still increases, the reason is the emission around Beijing is underestimated, and has been corrected. The accuracy of the SDz site changes negligibly. We believe that the reason is that the horizontal grid resolution of 50 km is not high enough to distinguish between two very close observation sites with different variation. This problem could be solved if we use a model and emissions inventory with higher resolution.

We also conduct the Monte Carlo simulation to quantify the uncertainty of
the total bottom-up emission and the inverse emission inventory in China.
The lognormal distribution is assumed, and the standard deviation is
calculated by combining the root mean square error between observation and
simulation with standard deviation of the inventory. Monte Carlo simulations
with randomly selected values within the PDFs are repeatedly implemented
10 000 times. The uncertainty in Chinese BC bottom-up emission and inversed
emission inventory at 95 % are obtained, as shown in Fig. 10. The mean
value, 2.5th percentile value, and 97.5th percentile value are 1570, 321,
and 5138 Gg (bottom-up) and 2650, 1114, 5471 Gg (inverse emission),
respectively. Therefore, the uncertainty of these two emission inventory are
about [

Streets et al. (2003a) estimated the 1.05 Tg BC emission in China for the
year 2000 with

An inverse modeling system is developed for BC emissions in an online-coupled chemical weather forecasting system, GRAPES–CUACE, using the inexpensive EnOI methodology. The emissions sampling strategy is discussed and improved. With its time correlation strategy, the ensemble forecast can have a larger spread to include the observations. The effect of localization in the analysis is also studied. With reasonable localization, the effects of sample error and spurious correlations are reduced.

BC aerosols in China are simulated and compared to surface measurements, with
the goal of deriving top-down BC emissions bias estimates. We conduct 1-year-long simulation for 2008, driven by the current Chinese bottom-up BC
emissions inventories. Comparison of the model results to observations at
background and rural sites evaluates the bottom-up inventories. The simulated
average monthly mean BC concentration in January for all rural and background
sites is 1.152

Applying top-down emissions estimates, the simulated average annual mean
concentration at rural and background sites for January is improved to
3.282

This work is supported by the National Basic Research Program (973) (2011CB403404), the National Natural Scientific Foundation of China (41305117), Basic Research Fund of CAMS (2013Y005) and the National Natural Scientific Foundation of China (41205081). Edited by: J. Brandt