The equations solved in the model have the form ∂qi∂t=-u∂qi∂x+v∂qi∂y+σ˙∂qi∂σ+Kx∂2qi∂x2+Ky∂2qi∂y2+∂(Γ2Kz∂qi∂σ)∂σ+Pi-Qi, where qi is the mass mixing ratio (kg kg-1) for the species i, qi=ci/ρ, where ci is the mass concentration (kg m-3) and ρ is the density of air (kg m-3), x and y are the horizontal coordinates (in meter along longitude and latitude directions), σ is the terrain-following vertical coordinate (σ=p/ps, where p is the present pressure and ps surface pressure) that ranges from 1 at the surface to 0 at the model top, u,v,σ˙ are the advection velocity in the x,y and the vertical directions of the σ-coordinates, Kx and Ky are horizontal diffusion coefficients that are assumed to be constant (Kx=Ky=6×104 m2 s-1) and Kz is the vertical diffusion coefficient based on the Monin–Obukhov similarity theory for the surface layer (Obukhov, 1971). The Kz profile is extended to the whole boundary layer by using a simple extrapolation (Hertel et al., 1995). Finally, Γ=dσ/dz (m-1). Pi are the sources and Qi are the sinks for the species i.

Equation (1) is solved on a spherical grid with 1∘ × 1∘ horizontal resolution and 25 vertical irregular σ-coordinate levels in the reanalysis product presented here. The average depth of the first layer is ∼ 30 m, and consecutive layers gradually increase in depth towards the top layer, which ends at ∼ 18 km (70 hpa). Advection is calculated using a semi-Lagrangian scheme (Staniforth and Côté, 1991), with departure points calculated using the method of Ritchie (1987). Horizontal and vertical diffusion are calculated with a finite-element method (e.g., Bathe, 2006).

Aerosol microphysics are treated relatively simply in NAAPS. This is in response to the computational needs of an efficient operational forecast model, its operational requirements (e.g., forecast severe visibility reducing events) and the fact that in comparison with the uncertainties in source functions as well as transport meteorology, microphysics is relatively well constrained. Dry mass concentrations are forecasted with Eq. (1) and AOT for each aerosol species is computed assuming an effective particle size with respect to mass. Aerosol particles in NAAPS are treated as external mixture of the aforementioned species and do not interact with each other. With these assumptions, extinction and AOT can be calculated using bulk values of optical properties that have been derived from theory and observations. The calculations for scattering (bscat, m-1), absorption (babs, m-1) and extinction coefficients (bext, m-1), plus the integrated optical thickness (τ, unitless) are, respectively, bscat,i(λ,x,y,σ)=ci(x,y,σ)αscat,i(λ)fi[r(x,y,σ)]),babs,i(λ,x,y,σ)=ci(x,y,z)αabs,i(λ),bext,i(λ,x,y,σ)=bscat,i(λ,x,y,σ)+babs,i(λ,x,y,σ), and τi(λ,x,y)=∫10bext,i(λ,x,y,σ)1Γdσ, where αext, αscat and αabs are the mass extinction, scattering, and absorption efficiencies respectively (m2 g-1), and fi is a scattering hygroscopic growth factor.

The bulk mass extinction, scattering and absorption efficiencies, along with single-scattering albedo and asymmetry factor for the four aerosol species at wavelength λ=550 nm are given in Table 1. For ABF, dust and sea salt, the values are taken from the Optical Properties of Aerosol and Clouds (OPAC) database (Hess et al., 1998). The chosen coefficients for ABF are weighted towards the more absorbing aerosol particles that are generated by less developed countries that dominate global aerosol fields (Dubovik et al., 2002). Optical properties for smoke are treated similarly, with both empirical derivations and theory derived from Reid et al. (2005a, b).

The effect of humidity on particle light scattering for each aerosol species is represented by the Hänel (1976) formulation of the hygroscopic growth factor fi(r) (unitless), defined as fi(r)=(1-r)(1-ro)-γi, where r is the relative humidity, γi is an empirical species-dependent exponent and ro is the reference relative humidity that is set equal to 30 %. In NAAPS, γi is taken as 0.5 for ABF particles assuming 40 % sulfate and 60 % organic aerosols. In comparison, γi is 0.63 for sulfate (Hänel, 1976), 0.18 for smoke (Reid et al., 2005b), 0.46 for sea salt (Hegg et al., 2002; Ming and Russell, 2001) and zero for dust (Li-Jones et al., 1998). A maximum allowed r is 95 %. We assume absorption αabs is not affected by humidity.

Dry deposition to the surface is accounted for through a decrease of the aerosol concentration in the lowermost model layer, assuming a dry deposition flux FDDi=c1ivdi, where c1i is the mass concentration (kg m-3) in the first layer above the surface for the species i, and vdi is the dry deposition velocity, which is a function of aerosol type and surface type.

For particle deposition over water, the dry deposition velocity vd is set to 0.0002 m s-1 for anthropogenic and biogenic fine particles, 0.0003 m s-1 for smoke loosely following the theoretical relation between over water vd and particle radius in Slinn and Slinn (1980), assuming bulk effective radius listed in Table 1 for the two types of aerosols. vd is set to 0.001 m s-1 over water for dust particles after tuning to minimize AOT corrections through the data assimilation process (more details in Sect. 2.4.2). Dry deposition of sea salt to open water is given by the formula in Slinn and Slinn (1980), assuming a dry mass mean radius near 1.5 µm, and written as vdss=CdU10, where Cd=1.3×10-3 is the drag coefficient, and U10 the wind speed at 10 m above the sea surface in m s-1.

For particle deposition over land, the method of Walcek et al. (1986) is used and the explicit expression for vd is the same as in Christensen (1997; Eq. 9), which is a function of surface friction velocity and Monin–Obukhov length, which is a measure of the stability of the surface layer (Obukhov, 1971, Eq. 26). This is written as

vd=u∗a1+-300L2/3forL<0u∗aforL>0, where u∗ is the surface friction velocity in m s-1, a=500 (except for a forest with leaves, where a=100) and L is the Monin–Obukhov length. vd is calculated using Eq. (9) for all the aerosol species in the model.

Gravitational settling is also applied to the aerosol particles in the model. Dry deposition is only applied in the lowermost model layer, whereas gravitational sedimentation takes place within the whole vertical domain except the lowermost model layer, as it is taken into account in vd.

The wet deposition of particles is assumed to be similar to that for sulfate aerosol, based on a simple scavenging ratio formulation (e.g., Iversen, 1989). The scavenging coefficient is calculated in the same way as in Witek et al. (2007), as a function of the precipitation mass flux with different below-cloud and in-cloud scavenging ratios, written as Wσ=ΛbcHPaσρwbelow cloud scavengingΛcHPσρwin cloud scavenging, where Paσ and Pσ (kg m-2 s-1) are the total downward flux densities of precipitation mass at a given σ-level below or in a precipitating cloud, respectively. H is an effective thickness for scavenging (set to 1000 m), Λbc=1×105 is the below-cloud scavenging ratio, Λc=7×105 is the in-cloud scavenging ratio and ρw is the density of water.

Dust emissions occur whenever the friction velocity exceeds a threshold value, snow depth is less than a critical value, and the surface moisture is less than a critical value (Westphal et al., 1988). The dust emission flux follows the equation Fdust=cefu∗4, where ef is the erodible fraction of a grid box (unitless), u∗ is the surface friction velocity with the threshold value of 0.6 m s-1 for dust mobility, and c is a scaling constant of 4.5×10-7 g m-2 s-1. In the operational version of NAAPS, the erodibility map is empirically derived from the United States Geological Survey Land Cover Characteristic Database and Total Ozone Mapping Spectrometer Aerosol Index values (Walker et al., 2009). While in general the operational version of NAAPS has good dust scores, NAAPS clearly has a high bias for dust for the Sahara. For the reanalysis, the use of Ginoux et al. (2001) dust sources mitigated much of this bias. The Ginoux et al. (2001) erodibility map associates dust sources with topographic depressions and has many of the same features as seen in Westphal et al. (1988), yet its geologic input data tightened individual source areas.

Regional source tuning is also applied in the NAAPS reanalysis, which is described in Sect. 2.4. Dust is emitted into the bottom two layers of the model (below 100 m) when friction velocity exceeds the threshold and surface wetness is below a critical value (0.4). Then, dust is transported by model dynamics both horizontally and vertically in the boundary layer and the free troposphere. Dust removal includes sedimentation, dry deposition and wet removal, which is constrained with CMORPH precipitation within the tropics. Dust is assumed to be totally hydrophobic and hence the hygroscopic growth factor is set to 1.

The sea salt component for operational NAAPS and the NAAPS reanalysis was developed by Witek et al. (2007). Sea salt emissions are driven dynamically by sea surface wind. The sea salt dry mass flux Fssa (kg m-2 s-1) from the surface is based on the whitecap method and the Monahan's formulation of the source function (Monahan et al., 1986), and has the empirical form Fssa=asU10bs, where U10 is the wind speed at 10 m above the sea surface in m s-1, as=1.37×10-13 and bs=3.41 for particles with diameters from 1.6 to 16 µm. Dry deposition of sea salt over water is proportional to the sea surface wind speed, following Slinn and Slinn (1980) and over land follows Eq. (9). Sea salt particles are assumed to undergo hygroscopic growth depending on ambient atmospheric relative humidity, following the growth rate shown in Eq. (6). The sea salt scattering coefficient is based on swelled particles, while absorption coefficient is assumed not effected by the swell.

The most significant change to NAAPS microphysics for the reanalysis is the development of a method to account for complex anthropogenic and biogenic species while not significantly increasing the computational cost of the model. Originally, the only anthropogenic emissions and predictive variables within NAAPS were SO2 and sulfate. However, organic species constitute one of the most important contributors to the mass of atmospheric aerosols (Zhang et al., 2007; Jimenez et al., 2009), and indeed commonly dominate the submicron aerosol mass and AOT. This organic aerosol mass, while having a significant component attributable to primary organic aerosol (POA) emission, is predominantly secondary organic aerosol (SOA; i.e., created in the atmosphere from volatile organic carbon (VOC) precursors in the gas phase, such as, isoprene, terpenes and aromatics; Zhang et al., 2007). These precursors are largely biogenic in origin. Ultimately, the complex chemical interactions between anthropogenic and biogenic emissions result in a photochemical soup that cannot be directly linked to a single origin.

For realistic simulation of AOT, primary and secondary organic aerosols must both be included in the NAAPS model in some form. To be consistent with the NAAPS reanalysis' philosophy of simple and tractable physics, the sulfur-related species has been replaced with a bulk ABF mass category to account for the entire class of anthropogenic and biogenic emissions and their secondary particle products. This species class includes all accumulation mode particles, including biogenic marine, outside of open biomass burning, as described in Sect. 2.2.7. The first component of this mixture is the original sulfur chemistry. Sulfate aerosols are produced by chemical processes in the atmosphere from gaseous precursors, mainly sulfur dioxide (SO2) from anthropogenic sources and dimethylsulfide (DMS) from biogenic sources. For NAAPS reanalysis, SO2 emissions are updated from Global Emissions InitiAtive (GEIA) version 1A (i.e., 1985) (Benkovitz et al., 1996) to Monitoring Atmospheric Composition & Climate/CityZen EU projects (MACCity) inventory 2005–2010 average (Granier et al., 2011; Diehl et al., 2012), which reflects the increased emission in India and China over the past decade and also includes monthly variation. DMS emission fluxes at the air–sea interface are computed using the Saltzman et al. (1993) parameterization, with the monthly DMS seawater concentrations from Lana et al. (2011). DMS are immediately converted to 95 % sulfur dioxide and 5 % sulfate in the model. SO2 chemistry follows Hoffmann and Calvert (1985), in which oxidation of sulfur solution (S(IV)) by hydrogen peroxide (H2O2) and dissolved ozone (O3) are considered climatologically. We assume background oxidants H2O2 and O3 are not depleted by reactions. Ultimately, sulfur chemistry accounts for roughly one-half of all non-biomass-burning fine-mode AOT.

Inclusion of POA in the NAAPS reanalysis is straightforward, including the major VOC species that act as precursors for the SOA. We apply the 2005–2010 monthly mean MACCity data base for anthropogenic (industrial and transport) emissions of POA and SOA precursors (Granier et al., 2011), the Bond et al. (2004) biofuels data with a monthly scaling factor based on Jeong (2011), and the Precursors of Ozone and their Effects in the Troposphere (POET) climatological monthly emissions inventory for biogenic VOCs (Olivier et al., 2003). For the actual SOA formation process, the Volatility Basis Set (VBS) approach has been adopted (Donahue et al., 2006; Ahmadov et al., 2012). This greatly reduces both the number of necessary precursor species and the number of SOA products from the vast numbers needed to explicit represent SOA formation and evolution by formulating the conversion process in terms of a limited number of precursor species and volatility classes (four in our case) for the reaction products. The reaction yields for the various VBS classes, upon which the approach ultimately depends, are derived from numerous chamber studies as cited, for example, in Ahmadov et al. (2012) and Donahue et al. (2006). Phase partitioning is done as per Pankow (1994).

To further simplify the inclusion of organic aerosols in the NAAPS model, both the POA and SOA are calculated in a “preprocessor” at model initialization. For the SOA, this includes calculation of the yield of SOA product mass from the emissions inventory VOC's, based on the VBS model, and the treatment of this mass as a primary aerosol emission, similar to the POA. Utilizing the similarity in microphysical and optical properties of organic aerosol (OA) and sulfate, the model carries POA and SOA together with sulfate as aforementioned “anthropogenic and biogenic fine”. This approach has some obvious shortcomings, but it carries minimal computational cost and has much improved the simulation of AOT, especially the model bias and correlation with Aerosol Robotic Network (AERONET) over India, China and eastern United States.

Biomass burning has a wide coverage globally, from the tropics to the high latitudes, and it significantly impacts the total light absorption budget (Bond et al., 2013). Unlike other aerosol sources that are meteorologically driven (e.g., dust and sea salt) or prescribed in a seasonal or monthly inventory (e.g., pollution), smoke emissions have significant variability that hinders easy parameterization. Configuring the NAAPS model with biomass-burning aerosols as a separate species permits explicit hypothesis testing about the sources, sinks and optical properties of these aerosols. Operational NAAPS has adopted the satellite-active fire hotspot-based approach through the Fire Locating and Modeling of Burning Emissions (FLAMBE1.0; Reid et al., 2009; Hyer et al., 2013). The model converts the smoke emission to total mass injected by multiplying by the fire size. This value is then divided by the area of the grid cell and the fire duration to create a flux as an hourly input to the model. FLAMBE can use satellite fire products from either geostationary sensors, which offer faster refresh rates and observation of the full diurnal cycle, or polar orbiters, which have greater sensitivity. Polar orbiting satellites have significant biases not only in their daily sampling pattern, but also additional artifacts from day to day shifts in the orbital pattern (e.g., Heald et al., 2003; Hyer et al., 2013). Over the reanalysis period, multiple changes in the geostationary constellation posed a challenge for consistency of the smoke source function. Therefore, a polar-only version of FLAMBE was created for the reanalysis.

Given that the NAAPS reanalysis coincides with the NASA Earth Observing System (EOS) system, MODIS-based fire products and emissions are applied. MODIS orbits have a 16-day repeat cycle, with daily coverage of the globe excepting small gaps between orbits at the Equator. Areas that are not covered one day are centered on the orbit the next. The Fire Inventory from NCAR (FINN; Wiedinmyer et al., 2011), which is also based on MODIS active fire detections, uses a 3-day moving average to account for gaps and orbital variations. After testing multiple coverage corrections, we found that for the reanalysis a simple two-day maximum (previous day and present day) fire signal largely mitigated orbital effects and thick clouds in a tractable way. This correction is consistent with the self-sustained nature of regional fire emissions, and further improves upon the scores presented in Reid et al. (2009).

Smoke injection height combined with boundary layer mixing has a strong influence on how smoke is dispersed. Most plumes are observed as constrained within the planetary boundary layers, especially within the tropics and subtropics (Tosca et al., 2011; Campbell et al., 2013). Large boreal fires can pump smoke to higher altitudes, though these fires constitute only a very small portion of the total fires and global budget of AOT (Fromm and Servranckx, 2003; Kahn et al., 2008). In NAAPS, smoke is injected into the bottom four layers of the model, which is approximately the bottom 400 m of the model. Tuning of injection height to match observed aerosol vertical profiles is feasible in regional studies (e.g., Wang et al., 2013). However, we use the uniform injection height in NAAPS, considering that boundary layer processes generally quickly mix aerosols well within the boundary layer or below the models significant inversion height to produce a result similar to the observations of Kahn et al. (2008).

The NAAPS prognostic variable is the three-dimensional aerosol mass concentration. A 2DVAR approach is adopted for AOT assimilation simply because AOT retrievals from MODIS and MISR are a column-integrated aerosol optical property. The 2DVAR AOT assimilation is realized through three steps:

Convert NAAPS mass concentration AOT:τbλ=Hm_τCm+ϵbλ,where τbλ is the background (prior analysis) AOT vector, Cm is the NAAPS mass concentration, and Hm_τ is the forward operator that represents the conversion of NAAPS mass concentration to AOT. εbλ is the error in τbλ introduced by the Hm_τ operator.

Both observational and model errors could contain systematic bias, either of which could be removed or minimized through pre-processing. For example, our quality assurance (QA) and quality control (QC) methodology (Sect. 2.3.3) attempts to remove systematic bias as much as possible from the AOT observations. Likewise the tuning process described in Sect. 2.4 attempts to remove systematic bias from the model background. Thus, both model background and observations are assumed to be unbiased in NAVDAS-AOT.

In NAVDAS-AOT, observational errors are assumed to be uncorrelated. Thus, only observational error variances are needed. The error variances for the gridded satellite AOT data are computed by the summation of instrumental error variances and sample error variances (Zhang et al., 2008). The instrumental error variance is estimated through the comparison of satellite and ground-based sun-photometer data as shown in Zhang and Reid (2006) and Shi et al. (2011a) for MODIS Dark Target, and Shi et al. (2014) for MISR aerosol products. The sample error variance measures the variance in the gridded mean (or the representative error variance). For a 1∘ latitude by 1∘ longitude grid, the sample error variance is derived by the spatial variance of the AOT data of the grid divided by the number of observations that are used in computing the gridded mean value.

The background error covariance is computed for any given two horizontal model grid locations m and n based on the following equation: Pbmn=[Sbm]1/2Cb1/2[Sbn]1/2, where Pbmn is the background error variance for horizontal grid locations of m and n. Sbm and Sbn are the model error variances at grid locations m and n, respectively. Cb is the horizontal background error correlation between the two grid locations. Similar to observational error variances, model error variances are also estimated using ground-based sun-photometer data, and the values are reported in Zhang et al. (2008). The Cbvalues are computed using the second-order auto-regressive (SOAR) approximation (Daley and Barker, 2001), Cb(m,n)=(1+Rmn/L)exp⁡(-Rmn/L). Here Rmn is the great circle distance between m and n. L is the horizontal error correlation length. The horizontal error correlation length is estimated through evaluating the differences in AOT between satellite observations and 6 h model forecasts as a function of horizontal distance. L is set to 200 km for this study based on Zhang et al. (2008).

The basis of input data for the reanalysis is operational MODIS Collection 5 AOT (Levy et al., 2007, 2010; Remer et al., 2005, 2008) and MISR AOT products (Martonchik et al., 2009; Kahn et al., 2009, 2010). MODIS Deep Blue for Collection 5 is not used here due to bias issues, but it is expected that improvements in Collection 6 will be made and the data could be assimilated (Shi et al., 2013). Extensive QA and QC procedures applied to the MODIS C5 AOT are conducted as described in Zhang et al. (2006) and Shi et al. (2011a) for over water and Hyer et al. (2011) for over land. These QA/QC procedures are especially important for this application, because the analysis must be heavily weighted to the observations to allow assimilation for correction of errors such as missing dust and smoke sources. Under these circumstances, the impact of noisy data is large and proper filtering and correction of data is critical. QA/QC procedures implemented for MODIS and MISR AOT include (a) strict checks for removal of possible cloud contamination, (b) corrections for the lower boundary condition, such as wind speed to correct for white caps and specular reflection over water and surface albedo over land and (c) aerosol micro-physical corrections based on derived fine-mode fraction over water and regionally over land. This strict quality assuring and quality control procedure is necessary to remove outliers and minimize erroneous aerosol features in MODIS that would adversely impact the model and propagate through the system. Currently, the total global data loss through screening of MODIS is about 40 %, with a reduction of absolute errors of 10–30 % over water (Zhang et al., 2006; Shi et al., 2011a). over land, the QA/QC procedures reduce data volume by ∼ 60 % and improve the global fraction of MODIS AOT within 0.05 ± 20 % of AERONET (Hyer et al., 2011). The data are aggregated into a 1∘ × 1∘ grid that matches the model resolution where additional buddy checks are applied.

A benefit of a reanalysis is that observations that are not timely enough to be incorporated into an operational run can be utilized. Thus, while MODIS products are used in all versions of NAAPS, for the reanalysis we can make use of MISR. Though narrower in swath than MODIS, and thus providing less relative coverage, MISR has two key benefits. First, MISR is on Terra and its imaging swath is in the MODIS sun-glint region. Hence, MODIS plus MISR completes the MODIS swath with full coverage. Second, the MISR over land algorithm has an advantage over retrievals conducted with other sensors in its handling of the lower boundary condition, provided that AOT < 0.8. In particular, there are large spatially correlated discrepancies between the retrieved MODIS and MISR AOT in regions of high albedo as a result of deficiencies in the MODIS lower boundary condition (Shi et al., 2011b). Notable regions of discrepancy between MODIS and MISR include the Andes Mountains, Saharan, the Arabian Peninsula and Central Asia (Shi et al., 2011b). Further, MISR can retrieve AOT in desert region at high efficacy where the operational MODIS Collection 5 Dark Target products cannot, thus providing further coverage in desert regions. QA and QC procedures, including the use of MODIS cloud mask products to reduce cloud contamination in MISR data sets and applying various quality checks and empirical corrections on MISR level 2 aerosol products, are conducted to generate data assimilation (DA)-quality data sets (Shi et al., 2011c, 2014). Then the data are aggregated into a 1∘ latitude by 1∘ longitude grid.

Data assimilation using NAVDAS-AOT is used to produce a new analysis after every 6 h of NAAPS integration time. The MODIS and MISR level 2 aerosol products are typically acquired in a 6 h range centered on the nominal valid time of the analysis (i.e., 00:00, 06:00, 12:00 and 18:00 UTC) from NASA data servers. Then QA/QC processes convert MODIS and MISR level 2 data into filtered, corrected and aggregated AOT observations with associated uncertainty estimates for assimilation in NAVDAS-AOT. After QA/QC processes, the general pattern of data coverage from MODIS and MISR for each assimilation cycle is shown in Fig. 1. The observed geographic pattern is attributed to the fact that MODIS and MISR AOT retrievals are limited to daytime and a limited range of sun-sensor geometries. The longitudinal range for which MODIS and MISR data available in a given assimilation cycle are limited because Terra and Aqua are in sun-synchronous orbits with equatorial overpass times of 10:30 and 13:30 local solar time, respectively.

For the MODIS sensors, overlapping coverage between Terra and Aqua over the 6 h data acquisition period does occur and a mean of Terra and Aqua weighted to the number of level 2 retrievals from each sensor. The contribution of each individual sensor to the total volume of the MODIS DA-quality data is about 50 % on average, although this number is highly variable on the 6-hourly basis, with the variability depending on the observability of the sensors (cloudy vs. non-cloudy, land vs. ocean, etc.). Because of its narrower swath compared to MODIS, the data volume of the MISR DA-quality data is only about 22 % on average of that of MODIS. Approximately half of the MISR DA-quality data overlaps with MODIS. When overlapping of MISR and MODIS 1∘ × 1∘ 6-hourly DA-quality data occurs, the mean of the two is taken for final assimilation purpose.

The seasonal geographic distribution of the total number of 6-hourly 1∘ × 1∘ fused MODIS and MISR DA quality AOT data averaged over 2003–2013 is shown in Fig. 2 (left column). Areas with high cloud coverage, including the Intertropical Convergence Zone and the subtropical stratus cloud deck regions, have relatively less data. In the polar regions, cloud contamination often exists in satellite-retrieved AOT data, leading to elevated AOTs. The Southern Ocean is an example of cloud-enhanced MODIS AOT, for instance (Toth et al., 2013). As a result, high-latitude AOT data are filtered out in the QA/QC process. The cutoff latitudes for AOT data to be assimilated are 40∘ S over water for the Southern Hemisphere and 80∘ N for the Northern Hemisphere. In addition, because MODIS and MISR AOT observations are only available during daylight, and thus there are no observations during polar nights, this results in more data counts in boreal summer than in boreal winter. Figure 2 also shows that areas with bright desert (e.g., Saharan, the Arabian Peninsula and Central Asia) or snowy/icy surfaces (e.g., Andes Mountains, Greenland and high latitude in boreal winter) have relatively less data to be assimilated, as these regions are mainly filled in by MISR retrievals that have a revisit time of 7 days on average rather than a revisit time of 1 day by MODIS.

The start date of the reanalysis is 1 January 2003, based on the availability of the observational data used in the reanalysis. Terra MODIS and MISR AOT data are first available in March 2000, and Aqua MODIS AOT is first available in July 2002. An additional consideration is CMORPH precipitation data, which is used to replace model precipitation within the tropics, is not available until December 2002. Since the required spin-up time for the aerosol model is 1 month, the reanalysis starts at 1 January 2003. Figure 3 shows the time evolution of 6-hourly data counts of the global MODIS, MISR and the fused 1∘ × 1∘ grid DA quality AOT in dots and their center-point 30-day-running average in solid lines. Throughout the reanalysis time period (2003–2013), the data counts of the DA-quality data are relatively stable, despite small dips in December 2003 in both MISR and MODIS and October 2008 in MISR due to the upstream data being unavailable. The data count of the fused MODIS and MISR DA-quality data is about 3800 during boreal summer and 2400 during boreal winter, on average. This essentially follows the seasonal variation of the MODIS DA-quality data count, which makes up about 80 % of the total fused MODIS and MISR DA-quality data. Half of the remaining 20 % is attributed to MISR alone and half is attributed to the overlapping MISR and MODIS DA-quality data. The seasonal variation of data volume is mainly related to the fact that more AOT data are discarded for the Southern Hemisphere high latitudes than the Northern Hemisphere high latitudes as a result of cloud contamination, and no observations are available during polar nights (Fig. 2).

The AERONET (http://aeronet.gsfc.nasa.gov), a ground-based global-scale sun-photometer network, has been providing high-accuracy measurements of aerosol properties since the 1990s (Holben et al., 1998, 2001). AERONET instruments measure sun and sky radiance at several wavelengths, ranging from the near ultraviolet to near infrared during daytime. It is often used as the primary standard for validating satellite products and model simulations (e.g., Kahn et al., 2010; Levy et al., 2010; Colarco et al., 2010). Since there are no AERONET data at 550 nm, measurements from multiple wavelengths (380 to 1020 nm) were used to estimate both fine- and coarse-mode AOTs at 550 nm, based on the spectral deconvolution method (SDA) of O'Neill et al. (2001, 2003). Extracted fine- and coarse-mode AOTs from AERONET AOTs are then compared to ABF plus smoke and sea salt plus dust, respectively. The SDA product has been verified using in situ measurements (Kaku et al., 2014) and has been shown to be able of capturing the full modal characteristics of fine and coarse particles while avoiding the uncertainties that come from using static diameter thresholds, at 0.8 or 1.0 µm, for example. Further, the SDA has also been shown to eliminate any potential cloud bias in fine-mode AOTs from AERONET (Chew et al., 2011), although thin cirrus contamination into the coarse-mode AOT can still be problematic in some regions such as Southeast Asia and Equatorial Africa (Chew et al., 2011; Huang et al., 2011).

Only cloud-screened, quality-assured level 2 AERONET data are used in this study (Smirnov et al., 2000), and the sites are marked with black dots in Fig. 4. Within the reanalysis time period, nearly 600 regular sites provided valid observational data. AERONET Distributed Regional Aerosol Gridded Observation Networks (DRAGON) observations are concentrated over a small area and a short period of time, and they are excluded from this study to avoid the effect of uneven sampling on the results from the statistical analysis. Spatially, the 1×1∘ grids in which the AERONET Level 2 data fall within are identified, and the model AOT is sampled from these identified model grids. Temporally, AERONET level 2 data are binned into 6-hourly intervals centered at the model synoptic output times of 00:00, 06:00, 12:00 and 18:00 UTC and then averaged within the bins. The model AOT at 550 nm is sampled consistently with AERONET: we extract the model AOT at a site using only times when AERONET had measurements. A second approach is tested, in which the model data are interpolated onto AERONET observation times. Validation results from the two methodologies are similar.

Empirical regional tuning of smoke and dust emissions is based on the fine- and coarse-mode AOT comparisons with AERONET. The globe is divided into 16 regions, as shown in Fig. 4, each having their own distinct aerosol characteristics. For example, South America, southern Africa, peninsular Southeast Asia and insular Southeast Asia have a prevailing smoke aerosol species during burning seasons, while northern Africa and Southwest Asia are dust dominated. East Asia and Indian Peninsular have mixed dust and pollution. Regional emission tuning factors were generated by using the regional bias and slope of the linear regression between pairwise NAAPS and AERONET AOT. This is done for 2009–2011 when AERONET data is more abundant than earlier years. Seasonally, data are grouped into the boreal winter–spring (December to next-May) and boreal summer–fall (June to November) time periods. These bi-seasonal temporal stratifications account for the major monsoonal and climatic shifts in the atmosphere while preserving major aerosol seasons such as, for the boreal summer/fall, the August–October biomass-burning seasons in southern Africa, South America and maritime continent, the June–August African dust season, and the United States and European summer haze seasons.

Regional emission factors, in the form of linear scaling factors applied to the original source functions for smoke and dust, are derived for each aerosol active season for the 3 years. For a single tuning factor, it differs slightly from year to year and season to season to a certain range. An average over the six seasons is taken to generalize this tuning factor for the reanalysis. The model is then run using the corrected emissions and the results are validated regionally against AERONET to determine whether the tuning improved bias, correlation, and root mean square error (RMSE). Additionally, the fine-/coarse-mode AOT time series of NAAPS and AERONET are reviewed for each site in the region to ensure the tuning is sensible. This process is repeated iteratively to refine the tuning. In Table S1, the values of the regional multipliers for smoke emission based on the 2-day maximum MODIS-only FLAMBE data base are listed. Also provided are the regional multipliers for soil erodibility, which are used to modify the dust source (Ginoux et al., 2001). The tuning factor for soil erodibility changes twice over the 11 years to accommodate the land surface parameterization changes in the meteorological analysis.

The total number of operational AERONET sites has grown to over 300 in recent years. However, the network's global coverage is uneven with the majority of sites located over land where they are easily accessible. The available AERONET data are often not representative of major aerosol impact regions, and it does not optimally sample for the biases that remote sensing products may have (Shi et al., 2011b). In particular, open oceans have few AERONET sites.

In regions with sparse AERONET data coverage, aerosol sources and parameters, such as sedimentation and dry deposition for ocean regions, are tuned using satellite AOT assimilation correction/increment fields. The monthly means of the daily AOT corrections (i.e., the difference between the assimilation posterior and the model prior) are a good indicator of the model performance globally. The correction maps can be used to quickly identify geographic regions where the model succeeds or does poorly. A region in which the data assimilation consistently suppresses aerosol mass could indicate a region with excessive aerosol emissions, or deficient removal, with the assumption that aerosol transport has much smaller uncertainty.

Since satellite products have uncertainties, especially over land, we rely on source corrections inferred from AERONET except where there are no representative sites close to the known source area (e.g., southern African biomass-burning region). Over the ocean where AERONET has only a few sites globally, satellite data assimilation plays an irreplaceable role, not only because of the good spatial and temporal coverage of satellite AOT data, but also because of its much smaller uncertainty compared to the over land AOT product (Hyer et al., 2011). Dust dry deposition velocity over water is tuned based on the AOT correction over the tropical Atlantic where African continental dust outflow is located, and is set to 0.001 m s-1. To minimize the AOT correction over the global ocean, especially high-latitude regions where surface wind is large, we also update the sea salt dry deposition velocity over water from a constant to a function of surface wind speed following Eq. (8). This effectively reduces the negative AOT correction over high-wind regions. This approach does not account for possible sources of error, including sea salt emission parameterization, biases in surface wind that drives emission and biases in boundary layer relative humidity that affects hygroscopic growth of the sea salt particles. In particular, our approach assumes that meteorological fields are correct, and implements correction solely to the uncertain parameters of aerosol sources and sinks.

Over the reanalysis period (2003–2013), the number of AERONET observations that can be paired with model data gradually increases with time (Fig. 6 top). The daily volume of global 6-hourly AERONET data has more than doubled in 2012 compared with 2003. The data count in 2013 decreases slightly due to the long processing time required for validating AERONET level 2 data (instruments need to be removed from the field and recalibrated; Smirnov et al., 2000). As there are more AERONET sites in the Northern Hemisphere than in the Southern Hemisphere and AERONET measurement only occurs during daytime, there are more AERONET observations during boreal summers than winters. Polar and high-latitude sites have few or no observations in winter, which raises a temporal sampling issue in validation for these regions. AERONET sampling also covaries with the seasonal AOT assimilation cycle, as high-latitude regions are less influenced by AOT assimilation during the wintertime.

Despite the uneven seasonal sampling, the 90-day-running average of the RMSE of reanalysis AOTs is quite stable throughout the reanalysis time period (Fig. 6 bottom), at around 0.1 for both fine- and coarse-mode AOTs and 0.14 for the total AOTs. Daily average RMSE can occasionally exceed 0.4.

Figure 7 provides the comparison of the pairwise 6-hourly reanalysis AOT and AERONET AOT for all of the available global sites during the reanalysis time period. The normalized data density is shown in color. AOT data from AERONET and the reanalysis are binned at a resolution of 0.01 and density of each bin is colored relative to the maximum density in the sample. Also shown are the basic statistics of the comparison: the total number of stations and the 6-hourly observations, bias, RMSE, square of the Pearson correlation coefficient (r2) and the linear regression parameters of the Theil–Sen method (Theil, 1950; Sen, 1968). The slope of the Theil–Sen linear regression is defined as the median of the slopes determined by all pairs of two-dimensional sample points. It is a robust linear regression that is insensitive to outliers and more accurate than the least-squares regression for potentially skewed data. For reference, also shown is the linear least-square regression line, which is more sensitive to outliers.

For both JJASON and DJFMAM, the global reanalysis fine-mode AOT has a small positive bias of slightly less than 0.01, while the coarse-mode AOT has a negative bias close to -0.02. The resulting bias for total AOT is -0.01. It is noteworthy that perhaps a portion of the AERONET coarse-mode bias is due to cirrus contamination (Chew et al., 2011), which will be mitigated in the next major revision of AERONET data. The RMSE values for both fine- and coarse-mode 6-hourly AOTs are ∼ 0.1, except that the RMSE of the coarse AOT is a little higher (0.11) during DJFMAM and a little lower during JJASON (0.08). The seasonality of RMSE for coarse-mode AOT is more apparent than that of the fine-mode AOT, which is consistent with Fig. 6. RMSE for the total AOT is 0.14 for both seasons, consistent with Fig. 6 as well. r2 is close to 0.65 for fine-mode AOT and close to 0.61 for coarse-mode AOT for both seasons. r2 for the total AOT is about 0.7, which is slighter better than the individual fine-/coarse-mode AOTs. The slope of the Theil–Sen regression lines is greater than 1 (around 1.3) for the fine-mode AOT, less than 1 (around 0.8) for the coarse-mode AOT, and very close to 1 for the total AOT for both seasons. All of the above statistical numbers indicate that the fine-mode AOT has a small high bias while the coarse-mode AOT has a small low bias on average and globally. There is little seasonal difference in the mode statistics (fine, coarse and total modes) for the whole globe.

As monthly data is often used in climate studies, we also evaluate the reanalysis monthly averaged AOTs (Fig. 8). Monthly averages are obtained only when the total number of 6-hourly AERONET data exceeds 10. For validation purposes, the monthly average reanalysis AOT is calculated based on the available 6-hourly data that can be paired with AERONET data. With the high-frequency signals (e.g., daily variability) smoothed out, the monthly average exhibits a better match with AERONET data over all. For both seasons and all modal AOTs, the monthly averages in the scatter plots are more aligned with the 1 : 1 lines, RMSE is roughly 50 % lower (0.07 for total AOT, 0.05 for fine- and coarse- mode AOTs) and r2 about 0.2 higher on average (with a maximum of 0.90 for the total AOT in DJFMAM and a minimum of 0.74 for the coarse AOT in JJASON). While absolute bias is unaffected by averaging, there appears a slope bias in linear regression results. Sites that may have a low background punctuated by severe events will appear in the regression differently from sites with a consistent but high background. This results in slope bias in regression of monthly averaged AOT values, demonstrating the dangers of applying monthly mean data to downstream calculations such as radiative forcing. Such calculations need to be conducted at the finest spatial and temporal scales achievable, with accounting for resolution effects.

Figure 9 shows the cumulative distribution function (CDF) of AOT errors compared with AERONET for total, fine and coarse AOTs, respectively, using 6-hourly data. As a reassurance, the CDF of AOT errors compared with MODIS and MISR DA-quality data is also shown. Because the seasonal differences for the global validation statistics are small, the two seasons are combined for the CDF analysis. As expected, the reanalysis total AOT is in good agreement with MODIS and MISR DA quality AOTs, though slightly less agreement with MISR than MODIS is found as the relative number of MISR data involved in AOT assimilation is much less. More than 95 % of the reanalysis total AOT has an AOT error falling in the AOT error range of [-0.05, 0.05] compared with MODIS or MISR. The reanalysis AOT has larger errors with respect to AERONET. The crossing points of the CDF curves and the zero AOT error line (and the -0.1/+0.1 error lines) show that about 35 % fine-mode AOT has a low bias (4 % with error less than -0.1) and the other 65 % has a high bias (6 % with error greater than 0.1) compared to AERONET. For coarse-mode AOT, about 60 % has a low bias (7 % with error less than -0.1) and 40 % has a high bias (2 % with error greater than 0.1). For the total AOT, about 44 % has a low bias (10 % with error less than -0.1) and 56 % has a high bias (8 % with error greater than 0.1). On average the fine AOT has a slightly high bias and the coarse AOT has a slightly low bias, which is consistent with the scatter plot result (Fig. 7).

Figures 10, 11 and 12 show box-whisker plots of the pairwise comparisons of regional reanalysis 6-hourly modal AOT vs. AERONET: percentiles marked in the plots are 95, 90, 75, 50, 25, 10 and 5 %, for the regions defined in Fig. 4 for 2003–2013. Also shown are regional mean AOTs designated by a diamond for AERONET and “+” for the reanalysis. Detailed statistics associated with Figs. 10–12 (including separation into two seasons) are provided in the Supplement. These include seasonal means and medians of the reanalysis and AERONET, along with reanalysis bias, RMSE, r2, Theil–Sen linear regression parameters and number of valid data points for each region and the globe.

In general, the reanalysis follows the regional variation found in AERONET for fine-mode, coarse-mode and total AOTs. For the fine-mode AOT, the reanalysis matches well with AERONET with respect to the regional means, medians, and variance. However, the results vary by region (Fig. 10). The regional means and medians are the same or slightly larger than those of AERONET for all regions, except East Asia and insular Southeast Asia, where the means are smaller than AERONET. The high AOT regions are the developing East Asia, Indian subcontinents, peninsular and insular Southeast Asia. These regions also have the highest RMSE values varying between 0.15 and 0.2, while RMSE values of other regions are all below 0.1. The low bias in mean fine-mode AOT in East Asia and insular Southeast Asia is mostly due to the model's inability to capture the magnitude of large fine aerosol events (e.g., extreme pollution and biomass-burning events). The r2 of most regions fall between 0.5 and 0.9. The best performing region is South America, whose r2 is greater than 0.8, indicating the reanalysis captures the temporal variation in fine-mode aerosols, which are attributed mostly to biomass-burning smoke. Regions with worse r2 include western continental United States (W. CONUS), northern Africa, Southwest Asia and insular Southeast Asia, with r2 around 0.4–0.5.

The coarse-mode AOT, overall, agrees less well with AERONET than the fine-mode AOT with respect to the regional means, medians, variances and correlations (Fig. 11). Many regions have generally very low coarse AOT; RMSE for these regions will be low, but r2 will also be low due to the small dynamic range. The most prominent high coarse-mode AOT regions are the dusty northern African and Southwest Asian domains. The moderate coarse-mode AOT regions are the dust-influenced Indian subcontinent, East Asia and Central America. These regions have relatively large RMSE (between 0.1 and 0.2), except central America (< 0.1), compared to other regions (< 0.1). Except for Southwest Asia, the oceanic region, boreal North America, W. CONUS and Australia, where the reanalysis mean coarse-mode AOT is comparable to that of AERONET, other regions show mean low biases. The low bias, relative to the mean AOT, is generally small, except for peninsular and insular Southeast Asia. The bias over these regions is attributed largely to the known thin cirrus contamination in AERONET L2 data (Chew et al., 2011; Huang et al., 2011). Thin cirrus cloud is a significant challenge for sun-photometer AOT measurement, as it is easily mis-categorized as coarse-mode aerosols by the instrument. The persistent occurrence of high thin cirrus cloud over these regions elevates the mean coarse-mode AOT and thus the mean total AOT substantially. For example, at Singapore, a representative site for the insular Southeast Asia, 34 % of AERONET L2 AOT data are found to be coincident with Micro-Pulse Lidar Network (MPLNET)-observed cirrus clouds (Chew et al., 2011). The estimated range of positive AOT bias in AERONET L2 data over Singapore, due to unscreened cloud presence, ranges from 0.03 to 0.06. Taking this estimated AOT bias of AERONET L2 data into account, the reanalysis coarse-mode AOT would be very close to reality. A similar situation exists for the peninsular Southeast Asia, based on the estimated cirrus cloud contamination in AERONET data at the regionally representative Pimai, Thailand, site (Huang et al., 2011).

The r2 of the coarse-mode AOT are less than those of the fine-mode AOT for most regions, except for northern Africa, Southwest Asia, Europe–Mediterranean and India, which have a strong dust influence. Insular and peninsula Southeast Asia have the worst correlations as expected, mostly because of the cirrus cloud contamination in AERONET data. Other regions, which have small AOT variations (e.g., dynamical data range less than 0.1), tend to have small r2 's, e.g., boreal North American and W. CONUS.

The total AOT, which is the sum of the coarse-mode AOT and fine-mode AOT, has a validation feature that combines the validation properties of the two AOT modes (Fig. 12). The regional variation of total AOT follows that of AERONET well. The variance of the reanalysis for each region is smaller overall than that of AERONET, suggesting the difficulty in capturing extreme events with the model and assimilation system and a tendency to underestimate the magnitude of extreme events and overestimate in very clean conditions. A smaller AOT variance is known to be a typical model behavior among aerosol models (Kinne et al., 2006; Sessions et al., 2015) and is a persistent challenge to the aerosol modeling community. The reanalysis does not perform as well with respect to mean bias and RMSE over East Asia, the Indian subcontinent and insular and peninsular Southeast Asia, where complicated aerosol environments often exist. For example, dust is often mixed with various kinds of pollutants over East Asia and the Indian subcontinent, which hinders satellite AOT retrievals and impacts model performance through AOT data assimilation. Over insular Southeast Asia, constant high cloud cover poses significant observability issues (Reid et al., 2013), reducing the availability of successful satellite retrievals of AOT, in addition to artificial high AOTs caused by cirrus contamination in AERONET data. This region also has a complicated fire regime that is systematically undersampled by the observations used to drive the smoke emissions in the model (Miettinen et al., 2013). The large discrepancies between the reanalysis and AERONET for coarse AOTs over insular and peninsular Southeast Asia affect the reanalysis means and medians for total AOTs, but to a lesser degree, since fine-mode aerosols are the dominant aerosol type for the these regions. Most regions have r2 between 0.5 and 0.8. W. CONUS has the smallest r2, which is about 0.376, among all regions, reflecting the challenge for the model to simulate the small variance of the AOT there.

Site-by-site validation of the NAAPS reanalysis was conducted relative to the International Cooperative for Aerosol Prediction (ICAP) Multi-Model Ensemble (ICAP-MME; Sessions et al., 2015) as a baseline. Overall, ICAP-MME was shown to outperform any individual models with regard to RMSE in 550 nm AOT forecast (Sessions et al., 2015). By ranking, the ICAP-MME was typically first or second against all models at individual sites using 1-year worth of data. Since most of the ICAP models include AOT assimilation as well, the NAAPS reanalysis was compared to the ICAP-MME. The 21 AERONET sites used in the ICAP-MME study were agreed upon by the world's major center developers, as the most representative of each region. The same two seasonal periods (DJFMAM and JJASON of 2012) are used. In Fig. 4, these sites are marked with red squares. The ICAP-MME is run daily at 00:00 UTC for 6-hourly forecasts out to 120 h. The best-available ICAP MME data (closest to analysis) for this comparison is the consensus mean of 6 h forecast at 00:00 UTC; thus, the NAAPS reanalysis is at an advantage in this comparison due to the lagged AOT assimilation cycle in the ICAP-MME.

Table 2 shows the name of each site, its location and the prevailing aerosol type, along with all statistics relating to the total AOT at 550 nm for the two seasons. The same statistics for fine- and coarse-mode AOTs are listed in Tables 3 and 4, respectively. The values of bias and RMSE are in bold, bold with underline and italic, depending on whether the reanalysis performance is the same, better or worse than the ICAP MME mean 6 h forecast, respectively. Over a majority of the sites, the total AOT of the reanalysis is the same or better than the ICAP-MME with respect to bias and RMSE. The exceptions are the Beijing and Solar Village AERONET sites. Singapore is uncertain, as the low biases in fine-mode AOT contributes less than half of the total low bias, implying the dominant bias is the coarse-mode AOT bias, which is affected by thin cloud contamination in AERONET data. Cases, where the reanalysis is the same or better than the ICAP-MME in bias and RMSE occur less for the coarse-mode AOT than for the total AOT. On the one hand, the total AOT is assimilated in the reanalysis while the coarse-mode AOT is not. So, the total AOT is better constrained with satellite observations. On the other hand, the ICAP-MME consensus mean for dust/coarse-mode AOT includes an additional independent aerosol model relative to the total AOT consensus (five vs. four models), which makes the dust AOT ensemble exhibit better performance among all the models compared with the total AOT ensemble performance (Sessions et al., 2015).

The AOT seasonal difference is very clear for sites with outstanding seasonal aerosol features. For example, higher total and fine-AOT values attributed to biomass burning are observed in JJASON over Alta Floresta, Rio Branco and Singapore and in DJFMAM over Chiang Mai. Seasonal differences are also found over Ilorin with higher AOT in DJFMAM relative to JJASON, due to both dust and biomass-burning activities. It is generally true that absolute bias and RMSE increase with increasing values of AOT, so a seasonal variation in bias and RMSE is also discernable for the sites with large seasonal AOT variations. r2 of the above sites in their biomass-burning seasons are generally very good (above 0.8 except for Singapore), indicating that the reanalysis captures the timing and variability of large smoke episodes quite well.

Overall, the sign of the bias and the order of magnitude of the bias and RMSE values for the selected sites are consistent with the regional evaluations in Figs. 10–12 (and the tables in the Supplement). For high AOT sites (e.g., Banizoumbou, Beijing, Chiang Mai, Gandhi College, Ilorin and Kanpur), the reanalysis generally has a low bias, as a result of the model and/or the data assimilation system being incapable of capturing the amplitude of high AOT events. An exception is Solar Village, though its dominant aerosol species, which is dust/coarse-mode aerosol, is also biased low in AOT during DJFMAM. Low bias in high AOT events is quite common among aerosols models (Kinne et al., 2006; Sessions et al., 2015). The discrepancy can arise solely as a function of spatial and temporal resolution: the average AOT for a grid cell in an aerosol plume will be systematically lower than the peak observed point AOT in that plume. However, shortcomings of aerosol sources or insufficient representation of near-source aerosol processes can also cause bias. Sometimes the discrepancy can be reduced by AOT assimilation, but the probability of a successful retrieval declines for higher AOT events, and this phenomenon is amplified by the application of AOT QA/QC procedures. The largest departure for both seasons in total AOT occurs over Beijing, where the coarse-mode bias contributes a little more to the total bias in DJFMAM and the fine-mode bias contributes a little more in JJASON. Among all sites, the maximum RMSE occurs over Beijing in both seasons for the total and the fine-mode AOT and in DJFMAM for coarse-mode AOT. JJASON RMSE is smaller for the reanalysis than for the ICAP-MME, implying that global models uniformly do not do well here. r2 of the coarse-mode AOT at Beijing is also the worst for both seasons, while r2 values for the fine and total AOTs are reasonable (0.54 in DJFMAM and 0.76 in JJASON for total AOT, and a little better for fine AOT). The frequent mixture of pollution, dust and clouds along with varying surface properties also hinders satellite retrievals, not only reducing the number of successful retrievals but also contributing to large errors in retrieved AOT (e.g., Shi et al., 2011b; Zhang et al., 2014). Similar situations exist for Ilorin, where a Sahelian biomass-burning system is often mixed with dust episodes in DJFMAM, and for Gandhi College and Kanpur, the two Indian sites, in both seasons.

For moderate to low AOT sites, including Cart Site, Chapais, Goddard Space Flight Center (GSFC), Minsk, Moldova, Monterey and Palma de Mallorca, the reanalysis performs well, with the biases falling between -0.02 and 0.02, RMSE values less than half of their site mean AOTs for all modes (all less than 0.07), and r2 between 0.42 and 0.85. Over Crozet Island, a remote oceanic site in the southern Indian Ocean, the reanalysis has a relative large high bias (compared to its very low mean) likely due to overestimation of sea salt. On the contrary, the fine-mode AOT has a slightly low bias, which may be an indication of insufficient DMS emission or too much removal.

Several sites are affected by similar aerosol sources at different distances, allowing us to examine transport phenomena using these sites. Banizoumbou, which is located deep in the Sahara, has the largest bias (negative) and RMSE, and the lowest r2 for the coarse and total AOT modes among all the African-dust-impacted sites. Capo Verde, located on an island off the west coast of northern Africa, has high coarse-mode AOT, but with much smaller bias and RMSE and high correlation (r2 is ∼ 0.88 for DJFMAM and ∼ 0.77 for JJASON for both total and coarse AOTs), benefiting from AOT assimilation. Farther downwind of northern Africa and across the Atlantic Ocean, Ragged Point in Barbados, shows even smaller biases and RMSEs and very high correlation (r2 greater than 0.81 for total AOT in both season, and for coarse AOT in JJASON). Palma de Mallorca, which is a receptor site for Saharan dust transported across the Mediterrean Sea, has bias, RMSE and correlation similar to Ragged Point.

The performance of the reanalysis has a tendency to increase with the distance from the source region, especially over water. The main reasons for this are (1) aerosol models normally have larger uncertainties in aerosol sources than aerosol transports (Kinne et al., 2003), (2) there is limited satellite AOT data over the bright desert regions for the model to assimilate (Fig. 2), while there are a lot more opportunities for the model AOT to be corrected by assimilation along dust transport paths and (3) the atmosphere acts to smooth out near-source variability that is often at finer scales than the effective resolution of the model. These effects can also be seen when comparing the reanalysis performance over Beijing and Baengyueong, an island site in South Korea downwind of Beijing, for both fine- and coarse-mode AOTs.