We expanded the variational assimilation system of a regional dust model by using size-resolved inversion. Dust emissions and particle-size distributions of a severe dust and sandstorm (DSS) in April 2005 were inversely optimized with optical measurements by the National Institute for Environmental Studies lidar network. The inversion results successfully compensated underestimates by the original model and increased the Ångström exponent around the DSS core by 13–17%, shifting the particle-size distribution to finer. The a posteriori size distribution was distinctly different between eastern and western source regions. In the western regions, dust emissions in the 3.19 and 5.06μm size bins increased considerably, and the peak size shifted from 5.06 to 3.19 μm, whereas in the eastern regions, emissions of finer particles (bins 0.82–2.01 μm) increased. Differences in vegetation and soil type and moisture between eastern and western regions might explain the characteristics of the inverted size distribution.
 Since soil dust is of natural origin, various atmospheric (e.g., wind speed) and surface factors (e.g., soil texture, soil moisture, snow cover, vegetation, and particle-size distribution) control the dust uplift flux, and complicate quantitative estimation of dust emission amounts by numerical models [Uno et al., 2006]. Particle-size distribution is one of the most important and also one of the most uncertain factors, because it affects the emission, lifetime, optical properties, and deposition of dust [Kok, 2011]. Shao developed a physics-based dust emission scheme to predict size-resolved dust fluxes from parent soil particle-size data. To drive his scheme adequately, however, accurate estimates of the atmospheric and surface factors are necessary, and lack of information about those factors makes accurate estimation of the size distribution of dust emissions quite difficult.
 Numerical inversion, which optimizes emission sources with observational constraints, is a powerful tool, and several inversion methods have recently been applied to Asian dust events [Yumimoto et al., 2007, 2008; Maki et al., 2011; Ku and Park, 2011]. Yumimoto et al. [2007, hereinafter Y2007] developed a 4-dimensional variational (4D-VAR) data assimilation system for a regional dust transport model (RAMS/CFORS), and successfully estimated emission amounts associated with an extreme dust and sandstorm (DSS) that occurred in late April 2005. However,Y2007applied the system only to the estimation of total dust emission amounts, and they did not address other details such as particle-size distribution of emitted dust, soil moisture, or threshold friction velocity. In this study, we expanded that model system by using size-resolved inversion and reexamined dust emissions and the particle-size distribution within the DSS. This is a very challenging because of limited observational information about dust-size distribution. We demonstrate the feasibility of the method and comparison of our results with the distribution of various environmental parameters (i.e., vegetation and soil properties). This study represents the first attempt to conduct a size-resolved inversion as part of an Asian dust study.
2.1. Assimilation System and Observation Data
 We used the RAMS/CFORS-4DVAR (RC4 [Yumimoto et al., 2007, 2008]) model and data assimilation system. RC4 consists of a forward dust transport model (RAMS/CFORS [Uno et al., 2003]), its adjoint model, and an optimization process. Size-resolved inversion was applied to the severe DSS of 26–28 April 2005. The basic set-up of the experiment was the same as that used byY2007. The simulation domain was centered at 37.5°N, 115.0°E on a rotated polar stereographic system, and covered all of China, Mongolia, and Japan. The model domain comprised 180 × 100 horizontal and 40 vertical grid cells with a horizontal resolution of 40 km. RC4 has 12 dust particle size bins whose effective radii (reff) are 0.13, 0.21, 0.33, 0.52, 0.82, 1.27, 2.01, 3.19, 5.06, 8.01, 12.7, and 20.1 μm. We describe the expansion to size-resolved inversion in subsection 2.2.
 The National Institute for Environmental Studies (NIES) lidar network consists of 23 sites in East Asia, where the vertical profiles of aerosols, including both backscatter intensity and the volume depolarization ratio, are measured with high vertical and temporal resolution [Sugimoto et al., 2008]. The volume depolarization ratio allows the contribution of mineral dust to the total extinction coefficient to be estimated [Shimizu et al., 2004]. We used the dust extinction coefficient measured at five sites (Beijing, Toyama, Tsukuba, Sendai, and Sapporo) as an observational constraint.
 In RC4, the dust extinction coefficient (βe) is calculated as follows:
where Φ denotes the dust mixing ratio; Δp, ρ, and g represent the layer thickness in pressure units, dust particle density (=2520 kg/m3), and the gravitational constant, respectively. The extinction efficiency factor Qe is a function of the size bin i, and is determined by Mie theory [Takemura et al., 2000]. In RC4, the extinction efficiency values assigned to each size bin are 0.86, 2.38, 4.10, 2.59, 2.73, 2.28, 2.34, 2.11, 2.17, 2.09, 2.07, and 2.05, from finer to coarser [see Satake et al., 2004, Table 1].
2.2. Expansion to Size-Resolved Inversion
Figure 1shows the size-resolved inversion method schematically. Previously (Y2007), the particle-size distribution of the dust emissions was fixed over the simulation domain and not modified in the inversion procedure. In this study, we expanded the scaling factorε (see below) to consider dust emission in each dust size bin. The dust emission flux E (kg m−2 s−1) of dust size bin i is represented as follows:
where u* and u′* respectively represent surface friction velocity and threshold friction velocity. The threshold friction velocity depends on soil texture and does not vary in size bins. C is a dimensional constant that is a function of snow cover, soil wetness, and soil texture; f represents the prescribed fraction of each dust size bin in the dust flux. Additional details of these constants are available in Uno et al. . εis a scaling factor and the dust emission flux is optimized at daily, grid, and size-bin resolutions. If we drop suffixi from ε, the dust emission inversion procedure is identical to that of Y2007.
 During transport, dry deposition and gravitational settling affects the size distribution within the DSS, and these depend on the dry deposition (vdry) and terminal (vgrav) velocities, as follows:
where Fdry and Fgrav denote the dry deposition and gravitational settling fluxes, respectively, ρair is the air density, and η is the viscosity of air (1.78 × 10−5 kg/m/s). In equation (5), the terminal velocity increases as the square of the effective radius reff. The dry deposition velocity also depends on the effective radius [Uno et al., 2003]. Thus, transport time (or transport distance) affects the dust size distribution.
 In the downwind region, lidar instruments measure the dust extinction coefficient of the DSS. Although lidar cannot directly capture the size distribution, the observed dust extinction coefficient includes information about the size distribution through the extinction efficiency (equation (1)). Background error correlations between size bins would also affect the inverted size distribution, but for simplicity we used the same background error values as Y2007 and ignored the error correlations. To summarize, the inverted size distributions are sensitive to the a priori size distribution of the dust emissions, gravitational settling, dry deposition, and the observed extinction coefficient.
3. Results and Discussion
 We applied the inversion experiment to a severe DSS that occurred in April 2005. On 26–28 April 2005, a DSS was caused by a cold front that accompanied a developing low pressure system over Inner Mongolia. The dust particles were transported eastward and were detected in China on 28 April and in Japan on 30 April (see Figure 4 in Y2007). Lidar measurements captured the dust layer at 2000–5000 m (see Figure 2 in Y2007). We compared the vertical profiles among the observation, a priori (without assimilation), Y2007(assimilation and non-size-resolved inversion), and a posteriori (size-resolved inversion) data at Beijing and three Japanese sites (Figure S1 in theauxiliary material). At the three Japanese sites, the a posteriori profiles are close to the observation profiles and comparable to the Y2007 profiles. At Beijing, the agreement of the a posteriori profile with the observation is better than that of the Y2007 profile because lidar measurements at Beijing provided an additional observational constraint in this study.
Figure 2a shows the horizontal distribution of the scaling factor, defined as the ratio of the total (integrated among all bins) a posteriori dust emission flux to the total a priori flux. The inversion result shows a considerable increase, compared with the a priori result, in dust emissions near the border between China and Mongolia (40–46°N, 92–104°E) and in central Mongolia (44–46°N, 102–108°E), and decreases in mountainous areas around Dund Sayhni Nuru (43.6°N, 103.8°E), the highest peak (2825 m a.s.l.) in the Gobi desert ranges (see Figure 4a). The horizontal distribution of the scaling factor is quite similar to that of Y2007 (Figure 1 in Y2007), but the size distributions differ greatly between Y2007 and our a posteriori results. We selected four regions where the dust emission amounts were considerably increased for further examination: region I, 43–45°N, 95–98°E; region II, 42–43.5°N, 99–102°E; region III, 44–46°N, 102–106°E; and region IV, 42–43.5°N, 107–110°E.
 In Figures 2b–2d, we show the particle-size distributions of the dust emissions in regions I–IV. Note that theY2007 distributions are identical to the a priori distributions. Because larger particles quickly fall out near the source region, the two largest size bins (12.70 and 20.13 μm) have little sensitivity and are not shown. The a posteriori size distribution differs obviously between the western (I and II) and eastern (III and IV) regions. In the western regions, the inversion considerably increased modeled emissions of the 3.19 and 5.06 μm fractions and shifted the peak emission size from 5.06 to 3.19 μm. In contrast, emissions of finer particle sizes are increased in the eastern regions. In region III, emissions of the 0.82–3.19 μm fractions are increased, but that of the 5.06 μm fraction is slightly decreased. In the easternmost region IV, the a posteriori size distribution shows the shallowest shape, and emissions of the 0.82–2.01 μm fractions are notably increased compared with the Y2007values. Even though the eastern regions are closer to the lidar observation sites, the size distributions are shifted toward finer particles. If the transport distance (and thus the amount of gravitational settling and dry deposition) dominantly affects the sensitivity of the size-resolved inversion, then finer sizes should be more abundant in the regions more distant from the observation sites (i.e., the western regions), and vice versa. Our result indicates that other factors (i.e., the observed extinction coefficient) in addition to the transport distance control the inversion results.
Figure 3 shows the horizontal distributions of the a posteriori dust aerosol optical thickness (AOT), the a posteriori Ångström exponent, and their increments, compared with the a priori values. The Ångström exponent, defined as the slope of the AOT between wavelengths of 440 and 870 nm, is commonly used as an indicator of the aerosol size distribution. The AOT is dense (>1.0) over eastern Japan (Figure 3a), and the assimilation compensated for the low a priori values. The AOT increment is as high as 0.6 over eastern Japan (Figure 3b). The DSS is characterized by small values (<0.18) of the a posteriori Ångström exponent (Figure 3c), indicating coarse dust particles. The horizontal distribution of the Ångström exponent reported by Y2007 is almost identical to the a priori distribution because they used a fixed size distribution. Compared with the a priori/Y2007 distributions, the a posteriori Ångström exponent shows greater horizontal variation, ranging from 0.07 to 0.18 (versus 0.11–0.14 for the a priori/Y2007 distributions) (Figure 3d); in particular, the Ångström exponent increment is reduced around the DSS front. In contrast, in the DSS core, assimilation led to finer size distribution and increases in the Ångström exponent by 0.15–0.25 (13–17%). The DSS front (altitude, 3000–5000 m), which is transported along the cold front, is at relatively higher altitude than the DSS core (2000–4000 m). This fact affects the variation of the a posteriori Ångström exponent; coarse particles transported at higher altitude have a longer lifetime than those transported at lower altitude.
 Volume size distribution (VSD) was calculated where the a posteriori AOT was larger than 0.8 on 30 April 2007 at 1200–1800 UTC (Figure S2). The Y2007 distribution (shape) is quite similar to the a priori distribution because Y2007 used a fixed size distribution. The offset between the Y2007 and the a priori result reflects increases in the dust emission amount. In the a posteriori result, the VSD is modified by increases of the 0.32, 0.82, 3.19, and 5.06 μm fractions, and reductions of the three largest fractions. These results cause the increases in Ångström exponent in the a posteriori result.
 Comparison of inverted and observed size distributions of dust emission fluxes is challenging because there are few direct measurements. To gain insight into the inversion results, we therefore examined several environmental parameters in the source regions (Figures 4b–4d). For these analyses, we used the soil group (Harmonized World Soil Database from the Food and Agriculture Organization [FAO] and the International Institute for Applied Systems Analysis [IIASA]: http://www.iiasa.ac.at/Research/LUC/External-World-soil-database/HTML/index.html), the Normalized Difference Vegetation Index (NDVI; MODIS/TERRA Vegetation Indices Monthly L3 Global 0.05Deg CMG data), and soil moisture (AMSR-E/AQUA Daily L3 Surface Soil Moisture from the National Snow and Ice Data Center [NSIDC]:http://nsidc.org/data/doc/daac/ae_land3_L3_soil_moisture.gd.html).
Figure 4b shows that most soils in the Gobi region (the Gobi desert, southern Mongolia, and Inner Mongolia) belong to the Kastanozem, Calcisol, and Gypsisol soil groups, but the dominant soil groups differ between the eastern and western regions. The soils of regions I and II are mainly Gypsisols (GY: soils with accumulations of secondary gypsum (CaSO4.2H2O)) whereas those in regions III and IV are dominantly Calcisols (CL: soils with accumulations of secondary calcium carbonate (CaCO3)). This distinct difference in soil types may explain the differences in the size distribution of the posteriori dust emission between western and eastern regions.
 The NDVI values tend to decrease from northeast to southwest (Figure 4c), and the regionally averaged NDVIs are 0.075, 0.069, 0.097, and 0.10 in regions I, II, III, and IV, respectively. Typically, bare soil has an NDVI value of around 0.025, and the value of light green-leaf vegetation is around 0.090 [Holben, 1986]. Vegetation in the eastern regions tends to be denser than in the western regions. Figure 4dexhibits soil moisture measured by AMSR-E. Regionally, the averaged soil moisture values are 85.24, 85.02, 88.75, and 80.42 g/cm3 in regions I to IV, respectively (Figure 4c); thus, the easternmost region IV is driest.
 As mentioned in introduction, threshold friction velocity u*′ is one of the most important parameters that affect dust emission flux. It is know that u*′ depends on not only particle size [Iversen and White, 1982], but also surface roughness and soil moisture. Denser vegetation increases surface roughness, causes a reducing of the wind shear stress, and then results in an apparent increase of u′* [Marticorena and Bergametti, 1995]. On the other hand, an increase of soil moisture increases u′* due to water films and wedges [Féccan et al., 1999]. Ishizuka et al.  measured dust saltation flux at gobi observation site in the Taklimakan desert, and showed that particle size distribution of sultation flux changed from dry to wet condition. These facts imply that variations in soil moisture and vegetation have the potential to affect size distribution of dust emission flux.
 During the period when the DSS occurred, the eastern regions are covered by denser vegetation. With difference in vegetation, we presume that u*′ tends to be higher in the eastern regions. In addition to difference in soil type, the denser vegetation may also be one explanation for the finer size distribution in the eastern regions through change of u*′. Moreover, the greater dryness of the soil in region IV (10% drier than soils in region III) may partly explain the flattened size distribution of the region IV emissions.
 In this study, we expanded the RAMS/CFORS-4DVAR assimilation system by using size-resolved inversion and reexamined the particle-size distribution and emission amounts in a DSS that occurred in April 2005. We then compared the a posteriori results with the previous size-fixed inversion results [Yumimoto et al., 2007], and we also examined environmental parameters (topography, vegetation, and soil properties) in the dust source regions. We summarize our results as follows.
 1. The a posteriori results compensated the underestimations of the a priori DSS emission results. The a posteriori dust emission amount was 18.9 Tg (Y2007; 17.6 Tg; a priori, 13.4 Tg).
 2. In the Y2007result, the Ångström exponent was little modified compared with a priori result, whereas in the a posteriori result the Ångström exponent increased by 0.15–0.25 (13–17%) around the DSS core, indicating that the size-resolved inversion produced a finer particle-size distribution.
 3. A posteriori dust emission fluxes showed distinct differences in particle-size distribution between eastern and western source regions. In western regions, the inversion considerably increased emissions of the 3.19 and 5.06μm fractions, and the peak emission shifted from the 5.06 to the 3.19 μm fraction. In the eastern region, the 0.82–2.01 μm fractions were considerably increased, and the overall size distribution was finer. In the easternmost region, in particular, the dust emission flux of the 5.06 μm fraction decreased considerably, and the distribution was flattened. Dust emissions in mountainous regions were decreased in the inversion result.
 4. There were distinct differences in soil group and NDVI between the western and eastern regions. The dominant soils in the western and eastern regions were classified in Calcisols and Gypsisols, respectively. NDVI tended to decrease from northeast to southwest, and denser vegetation was indicated in the eastern regions. These differences might explain the differences in the size distribution in the a posteriori dust emission. Moreover, the soil moisture content was the lowest in the easternmost region (10% drier than soils in region III), which might account for the flattened size distribution there.
 Despite limited observational constraints, the inversion results were promising, demonstrating the feasibility of the method. To make the inversion system more robust, in a future study additional observational constraints should be applied (e.g., multispectral observational constraints) and the results should be validated by various observations in both downwind and source regions.
 This study was supported by KAKENHI grants (21241003, 23840050 and 24740326) from the Japan Society for the Promotion of Science.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.