We developed a new ensemble-based data-assimilation system based on a global aerosol climate model and performed a 1-month assimilation experiment using satellite optical measurements from MODIS onboard TERRA and AQUA to estimate the direct radiative effect (DRE) of aerosols. Using the assimilated data field, monthly averaged optical thickness (AOT) was estimated to be 0.15 ± 0.030 (a 52.0% increase over a priori), and the root mean-square difference (RMSD) between modeled values and MODIS measurements was reduced by 28.4%. Independent validation using globally distributed AERONET measurements showed that the a posteriori data achieved better agreement with 82.5% of 80 AERONET sites. However, improvements in Ångström exponents were limited (50.0% of sites). Using the assimilated aerosol field, we modeled the aerosol DRE. A posteriori whole- and clear-sky DREs at the top of the atmosphere were estimated to be −1.1 ± 0.35 and −2.5 ± 0.49 W/m2, respectively, in May 2007 and were close to previously reported measurement-based estimates.
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 Airborne aerosol particles impact not only air quality but also climate by affecting the radiative budget and cloud microphysics [Solomon et al., 2007]. Recent advances in numerical modeling and aerosol observations have provided insight into these effects [e.g., Kinne et al., 2006; Yu et al., 2006, and references therein]. However, critical uncertainty remains in these estimates. The Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon et al., 2007] suggested that scientific understanding of aerosol radiative forcing was still at mid-low or low levels. In a comparison of 12 aerosol models, the AeroCom project [Textor et al., 2007] found that the discrepancies between models were sometimes larger than the discrepancies between models and observations. In a review of model- and measurement-based aerosol optical thickness (AOT) and the direct radiative effect (DRE), Yu et al.  suggested that model-estimated DRE varied widely but was approximately 30 to 40% less than measured values on average. This discrepancy was partially attributed to the poor understanding of the three-dimensional (3D) distribution of aerosols (including emission amounts), as well as prescribed aerosol optical properties and various aerosol processes. There is the need for further studies and improved models.
 One such improvement has been the use of data-assimilation techniques in chemical and aerosol models [e.g., Collins et al., 2001; Zhang et al., 2008; Yumimoto et al., 2008]. Data assimilation integrates numerical models and observations to obtain the optimal solution and reduce uncertainty. In terms of observations, data assimilation optimally interpolates and complements sparse observations with model results into complete four-dimensional (4D) space. In numerical models, observed information (e.g. mixing ratio and optical thickness) is reflected in the simulation via modification of initial condition or parameters, through statistic filtering (e.g. best linear unbiased estimate). Thus, an aerosol model integrated with observations through assimilation should provide comprehensive and optimized 4D distributions of aerosols and substantially advance our understanding of aerosol mechanisms and applied research. In this study, we developed a new ensemble-based data-assimilation system using the global aerosol climate model SPRINTARS [Takemura et al., 2005]. To verify the feasibility and performance of the system, a 1-month assimilation experiment in May 2007 was performed using satellite optical observations. Assimilation results were validated globally with observations by the NASA Aerosol Robotic NETwork (AERONET) [Holben et al., 2001]. The DREs of anthropogenic and natural aerosols were estimated in an on-line manner using the assimilated aerosol field.
2. Numerical Model, Observations, and Assimilation Method
 We used the Spectral Radiation-Transport Model for Aerosol Species, version 3.84 (SPRINTARS), a state-of-the-art global aerosol climate model [Takemura et al., 2005]. SPRINTARS is coupled with a general circulation model, the Model for Interdisciplinary Research on Climate (MIROC), developed by the Atmosphere and Ocean Research Institute of the University of the Tokyo (AORI)/National Institute for Environment Studies (NIES)/Japan Agency for Marine-Earth Science and Technology (JAMSTEC) [K-1 Model Developers, 2004]. SPRINTARS includes the major tropospheric aerosol components (carbonaceous, sulfate, soil, dust, and sea salt), and treats the direct, first indirect, and second indirect effect of aerosols in an on-line manner. The horizontal resolution is set to T42 (about 2.8°) with 20 vertical layers. We used the representative concentration pathways (RCPs) in 2000 as emission inventories [Lamarque et al., 2010] for both anthropogenic and biomass burning emissions of carbonaceous aerosols (black and organic carbons) and SO2, as well as the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis product [Kalnay et al., 1996], which nudges horizontal wind and temperature in MIROC. To perform an ensemble simulation, emissions and injection heights were randomly perturbed in each ensemble run. The perturbation coefficient for emissions was generated along a log-normal distribution, with mean = 1 and variation = assuming uncertainties. We assumed that emissions uncertainties were 500% for dust and sea salt, 350% for carbonaceous materials, and 130% for non-sea salt sulfate, based on the report of Bates et al. . They estimated normalized uncertainties of the various processes in prediction of column aerosol amounts based on model inter-comparisons, sensitivity studies, and expert opinion. Injection heights were randomly perturbed within ±1 model vertical grid, except for volcano emissions. We conducted a 5-day spin-up before the experiment to spread perturbations globally. Figure S1 in the auxiliary material shows the monthly averaged ensemble spread of total AOT.
 For assimilation data, we used the AOT at 550 nm from five aerosol products provided by Moderate Resolution Imaging Spectroradiometer (MODIS) observations from the NASA AQUA and TERRA satellites. AQUA and TERRA are polar orbital satellites that cross the equator at 13:30 and 10:30 local time (LT), respectively. To avoid cloud contamination, we assimilated observations of cloud fractions less than 0.7 between 70°S and 70°N. We assumed that observation errors were uncorrelated and assigned them at 0.03 ± 0.05τMODIS, based on the results of Remer et al. , where τMODIS denotes MODIS AOT. About 7,900,000 data were used in the experiment.
 NASA AERONET (http://aeronet.gsfc.nasa.gov/) provides global optical measurements of aerosols. We used AOT data (Level 2.0) from 80 sites, where enough measurements existed during the assimilation period, for an independent validation. The AOT at 550 nm was linearly interpolated from measured AOT at 500 and 670 nm.
2.3. Assimilation Method
 We applied a local ensemble transform Kalman filter (LETKF) [Hunt et al., 2007] to SPRINTARS. The LETKF is based on the ensemble Kalman filter (EnKF) [Evensen, 1994], and the LETKF (EnKF) assimilation process is summarized as
where xf and xa are aerosol mass mixing ratios of each aerosol component. Suffixes f and a represent forecast (a priori) and analysis (a posteriori), respectively. y denotes an observation (in this study, MODIS AOT: τMODIS). H is a linear observation operator that converts the aerosol mass mixing ratios into AOT values and then interpolates from model space into observation space. K is the Kalman gain defined as follows:
where Pf and R are the forecast and observational error covariance matrices, respectively. Pf is estimated and is evolved by the ensemble simulation. In LETKF, the Kalman gain is solved by the transformation method (i.e., eigenvalue decomposition) [Bishop et al., 2001], and the assimilation procedure is performed in divided local regions (i.e., localizations). Localization reduces computational cost and spurious error covariance among distance caused by sampling error due to the limited ensemble size [Miyoshi and Yamane, 2007]. We adapted the multiple inflation method [Whitaker et al., 2008] and set some tunable parameters based on the sensitivity analysis described below.
 We design an assimilation efficiency (AE) to estimate data assimilation performance. AE is determined in terms of the root mean-square difference (RMSD) defined as:
where y, o, and n are observations, model outputs, and number of data, respectively. AE is defined as follows:
where RMSDf and RMSDa denote the RMSD before and after assimilation, respectively. A positive (negative) AE indicates that the modeled values are close to (deviate from) the observations via the assimilation. AE = 100% indicates that a posteriori results completely agree with the observations.
3. Results and Discussion
 As mentioned in subsection 2.3, LETKF has several tunable parameters that affect assimilation performance. Before the 1-month experiment, we performed 2-week sensitivity experiments with reduced measurements, changing the parameters. One of the most important parameters is ensemble size (i.e., ensemble number). Insufficient ensemble size causes sampling error and filter divergence, whereas an ensemble size that is too large imposes needless computational cost. Another important parameter is localization scale, or the radius of the local region. Figure 1 shows the results of the sensitivity experiments. The smallest ensemble size shows much lower AE values than other sizes at all localization scales, thus indicating that a 10-member ensemble is too small to represent model error covariance. A larger ensemble size yields improved results, and the sensitivity analysis shows a monomodal structure with respect to localization scale. Generally, a larger localization scale needs a larger ensemble size to dampen the sampling error [Miyoshi and Yamane, 2007]. Compared to a 25-member ensemble, a 30-member ensemble showed little improvement (approximately 0.2% at radius 3), indicating that 25- and 30-member ensembles are large enough to dampen the sampling error, and more ensemble members are not likely to improve results significantly. In light of computational costs, we assigned a 25-member ensemble size and three-grid localization scale.
Figure 2 shows results of the 1-month assimilation experiment. In this figure, SPRINTARS results were sampled at MODIS measurement times and interpolated into the observation space. Figure 2d shows the increment between a posteriori and a priori values. The a posteriori AOT showed much better agreement with MODIS AOT than did the a priori estimate. The AE with MODIS AOT was 28.4%. The a posteriori global mean AOT increased from 0.069 to 0.10 and was close to that of MODIS (0.15).
 The assimilation mainly increased aerosol values over the Northern Hemisphere. In the Middle East and East Asia, dust increased considerably. Sulfate aerosols increased in industrializing areas, such as India and China. Over the North Pacific, dust, carbonaceous materials, and sulfate outflows from East Asia were enhanced and brought closer to the MODIS AOT. Over the North Atlantic, sulfate from North America increased, and the outflow path of Saharan dust shifted slightly to the south, with transport farther west, showing better agreement with MODIS measurements. An increased AOT in Central America reflects carbon from forest fires filling the gap between MODIS and a priori estimates. However, in Siberia the assimilation reduced carbonaceous AOT from forest fires. For sea salt, the a posteriori AOT increased in the tropics, decreased at high latitudes, and showed a relatively spatially uniform distribution (Figure S2). Recently, Jaeglé et al.  integrated in situ measurements, MODIS, AERONET, and GEOS-Chem models and speculated that sea salt emissions depend not only on wind speed but also sea surface temperature (SST): a higher SST favors sea salt emissions and vice versa. Our assimilation results were consistent with their results with modified sea salt emissions [Jaeglé et al., 2011, Figures 8 and 9]. A posteriori globally averaged AOT of total, dust, sulfate, carbonaceous materials, and sea salt aerosols were 0.15 ± 0.030 (152.0% of a priori), 0.044 (159.7%), 0.042 (200.0%), 0.026 (186.1%), and 0.040 (106.6%), respectively.
Figure 3 shows the independent validation using AERONET measurements. AE values at each site are shown in Figure 3a (center panel). The assimilation achieved improvements at 66 (82.5%), 69 (86.3%) and 62 (77.5%) of 80 sites, for AE, mean AOT and correlation coefficient, respectively. Positive AEs are distributed at sites over the Northern Hemisphere where larger increments of aerosol amount are shown (Figure 2d). Figures 3b–3i compares a posteriori, a priori, AERONET, and MODIS AOT time series. A posteriori results showed better agreement with AERONET measurements than did a priori values. For heavy aerosol plumes especially, the assimilation considerably improved a priori underestimates (e.g., at Chen Kun Univ: Figure 3b; Carpentras: Figure 3e; and Cape San Juan: Figure 3f). Notably, at Solar Village, where few MODIS measurements are available because of the high surface reflectance of the desert, the assimilation agreements are much better. At Izana (Figure 3d), an overestimate during 8–13 May was corrected, mainly by reduction of dust AOT.
 Although the assimilation showed significant improvements at most AERONET sites, some sites, such as Mauna Loa (Figure 3h), had negative AE values. AOT was also overestimated in the a posteriori results, widening the discrepancy between measurements and a priori estimates. However, MODIS AOT was much higher than AERONET AOT, and the a posteriori results agreed better with MODIS AOT, thus indicating that the positive MODIS AOT bias led to a larger discrepancy, and the assimilation performed well. Similar degradations were found at sites such as Izana, with low AOT values (monthly AOT < 0.1), thus implying that further observational quality control (QC) and quality assurance (QA) [e.g., Zhang and Reid, 2006] are required in future studies. The coarse resolution also obstructs the effects of local terrain and emissions at sites in mountainous islands (i.e., Mauna Loa and Izana) and urban areas (especially in Europe). Poor improvements in inland Australia and South America reflect the paucity of MODIS measurements and insufficient ensemble spread, respectively.
 We also performed validations using Ångström exponents (440–870 nm) measured by AERONET (not shown). The assimilation resulted in positive AE values at 40 of 80 (50.0%) sites. We found limited improvements in Ångström exponents. In this study, we assimilated only AOT (i.e., optical column aerosol amounts). Each analysis increment of aerosol components (or bins) was distinguished or weighted by the forecast error covariance Pf (i.e., the ensemble spread) and each optical property of aerosol components (e.g., extinction cross-section) included in observation operator H (see equations (1) and (2)). This method curbed unrealistic adjustments (e.g., increase in sea salt over inland areas). In future studies, additional information (e.g., measurements of the Ångström component and fine-mode AOT fraction) will be assimilated to constrain the distribution of the analysis increment. Further studies of ensemble spread structure will also be required to estimate the appropriate error covariance between aerosol components.
Figure 4 compares a posteriori and a priori anthropogenic and natural aerosol increments of the DRE at the TOA. Shortwave negative DRE radiation was reduced considerably in East Asia, India, and North America because of an increase in sulfate aerosol. Reductions in Central America and South Africa mainly resulted from increases in carbonaceous aerosols. However, a reduction in carbonaceous aerosols from Siberian forest fires resulted in an increase in the shortwave DRE over the north Pacific. An increase in the longwave positive DRE in East Asia, the Middle East, and the Sahel corresponded to increased dust, and an increase in sea salt increased the longwave DRE over the central Pacific. The a posteriori whole-sky longwave (shortwave) DRE at the TOA was 0.46 ± 0.087 (−1.5 ± 0.40) W/m2 and increased (decreased) by 77.3% (83.2%). We estimated the total whole-sky DRE at the TOA as −1.1 ± 0.35 W/m2.
Yu et al.  reviewed measurement- and model-based DRE estimates and assessed median values of measurement-based (model-based) estimates of the clear-sky DRE at the TOA in spring over ocean and land as −5.6 ± 0.20 (−3.5 ± 0.66) and −5.1 ± 0.26 (−3.2 ± 0.65) W/m2, respectively. Our a posteriori (a priori) clear-sky DRE estimates at the TOA over ocean and land in May 2007 were −2.5 ± 0.47 (−1.4) and −2.7 ± 0.52 (−1.5) W/m2, respectively. Although the assimilation brought the a posteriori DRE much closer to Yu et al.'s  estimates, large discrepancies still remained. Yu et al.  suggested that lower AOT, stronger absorption, and uncertainties in SPRINTARS optical parameters could possibly account for the discrepancies.
 We developed a new ensemble-based data-assimilation system using the global aerosol climate model SPRINTARS and performed a 1-month assimilation experiment using aerosol optical observations in May 2007. The experiment assimilated 7.9 million measurements made by MODIS/TERRA and AQUA. A posteriori AOT reduced the RMSD between MODIS AOT by 28.4% compared to a priori AOT and showed significantly improved independent validation with globally distributed AERONET data (82.5% of 80 AERONET sites showed better agreement). Meanwhile, Ångström exponent improvement was limited, with better agreement with only half of 80 sites. The assimilation mainly increased aerosols over the Northern Hemisphere (e.g., increased sulfate over developing countries and dust in the Middle East and East Asia). A posteriori sea salt increased in the tropics and decreased at high latitudes. Our best estimate of global AOT was 0.15 ± 0.030 (152.0% of a priori) in May 2007.
 Aerosol DRE was modeled in an on-line manner using a posteriori aerosol fields. The a posteriori whole-sky DRE at the TOA was estimated as −1.1 ± 0.35 W/m2 (−185.9% of a priori) in May 2007. For clear-sky, our a posteriori results estimated the DRE at the TOA over ocean and land as −2.5 ± 0.47 and −2.7 ± 0.52 W/m2, respectively, with the measurement-based estimates decreasing positive biases [Yu et al. 2006] by 25.0% and 33.3%, respectively. However, large discrepancies still exist. In addition to improvements in the model, additional observations (especially those that can distinguish aerosol species) and a new ensemble generation method, which takes model errors in transport and deposition processes into account, will be the next steps in improving the assimilation system.
 This study was supported by the Funding Program for Next Generation World-Leading Researchers by the Cabinet Office, Government of Japan (GR079) and Grant-in-Aid for Research Activity Start-up (23840050) by Japan Society for the Promotion of Science.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.