Mixing weight determination for retrieving optical properties of polluted dust with MODIS and AERONET data

Following the models and empirical values employed by Lin et al (2013), the bulk (ensemble-averaged) optical properties of the dust and soot particles can be obtained by weighting the probability distribution functions of dust-like aerosol and the number of monomers per aggregate. Under the external mixing procedure, the optical properties of polluted dust can be expressed as (Levoni et al 1997)

$$\begin{eqnarray}&&\langle {k}^{{\rm{e}}{\rm{x}}{\rm{t}},{\rm{s}}{\rm{c}}{\rm{a}},{\rm{a}}{\rm{b}}{\rm{s}}}\rangle =\displaystyle \frac{{w}_{{\rm{d}}}\cdot {k}_{{\rm{d}}}^{{\rm{e}}{\rm{x}}{\rm{t}},{\rm{s}}{\rm{c}}{\rm{a}},{\rm{a}}{\rm{b}}{\rm{s}}}+{w}_{{\rm{s}}}\cdot {k}_{{\rm{s}}}^{{\rm{e}}{\rm{x}}{\rm{t}},{\rm{s}}{\rm{c}}{\rm{a}},{\rm{a}}{\rm{b}}{\rm{s}}}}{{w}_{{\rm{d}}}+{w}_{{\rm{s}}}},\end{eqnarray} \tag{ 1 }$$

where ${k}_{{\rm{d}}}^{{\rm{e}}{\rm{x}}{\rm{t}},{\rm{s}}{\rm{c}}{\rm{a}},{\rm{a}}{\rm{b}}{\rm{s}}}$ and ${k}_{{\rm{s}}}^{{\rm{e}}{\rm{x}}{\rm{t}},{\rm{s}}{\rm{c}}{\rm{a}},{\rm{a}}{\rm{b}}{\rm{s}}}$ represent the bulk coefficients of extinction, scattering and absorption of dust particles and soot aggregates respectively; w_d and w_s are the number-density mixing ratio of dust and soot. On the basis of this definition, the SSA of polluted dust, ${\mathrm{SSA}}_{\mathrm{mixture}},$ can be correspondingly derived for the specific wavelength as below

$$\begin{eqnarray}&&\langle {{\rm{SSA}}}_{{\rm{mixture}}}\rangle =\displaystyle \frac{(1-{w}_{{\rm{s}}}){k}_{{\rm{d}}}^{{\rm{s}}{\rm{c}}{\rm{a}}}+{w}_{{\rm{s}}}{k}_{{\rm{s}}}^{{\rm{s}}{\rm{c}}{\rm{a}}}}{(1-{w}_{{\rm{s}}}){k}_{{\rm{d}}}^{{\rm{e}}{\rm{x}}{\rm{t}}}+{w}_{{\rm{s}}}{k}_{{\rm{s}}}^{{\rm{e}}{\rm{x}}{\rm{t}}}}.\end{eqnarray} \tag{ 2 }$$

Using the concept of the multi-channel retrieval technique of the Deep Blue algorithm (Hsu et al 2004, 2006), the database of look-up tables of TOA reflectance in visible spectral bands (0.412, 0.470, and 0.650 μm) of polluted dust can be constructed as the function of aerosol optical depth and single scattering albedo (${{\rm{AOD}}}_{{\rm{mixture}}}$ and SSA_mixture), as well as the mixing weight of dust and soot (${w}_{{\rm{d}}}$ and w_s). That is, the optical parameters of polluted dust can be obtained from the constructed database in terms of the multi-spectral TOA reflectance observed by the satellite sensor.

In the previous study (Lin et al 2013), a uniform spatial distribution of soot mixing weight has been obtained by including a point value of SSA/refractive index (REFI) from in situ measurement (known as the 'fixed ${w}_{{\rm{s}}}$ process'). However, the 'fixed ${w}_{{\rm{s}}}$ process' sometimes results in a large discrete jump of ${k}_{{\rm{d}}}^{{\rm{s}}{\rm{c}}{\rm{a}}}$ and ${k}_{{\rm{d}}}^{{\rm{e}}{\rm{x}}{\rm{t}}}$ of pure dust over the source regions. In addition, the determination of mixing weight is greatly limited by site location. The uniform distribution is also usually unable to describe the dust plumes. It is more sensible that the soot mixing weight could be changed with the number-density mixing ratio of dust particles. In order to overcome the shortage of the fixed ${w}_{{\rm{s}}}$ process, the values of ${k}_{{\rm{d}}}^{{\rm{s}}{\rm{c}}{\rm{a}}}$ and ${k}_{{\rm{d}}}^{{\rm{e}}{\rm{x}}{\rm{t}}}$ were constrained based on long-term observation of in situ measurements, such as the data of AERONET. It is referred to as the 'fixed ${k}_{{\rm{d}}}$ process' thereafter. By extracting the look-up tables from a pre-constructed database of polluted dust corresponding to the observation geometries and the auxiliary data of surface reflectivity, the soot mixing weight (${w}_{{\rm{s}}})$ can be determined in accordance with the MODIS spectral TOA reflectance (as the red cross symbol indicates in the look-up table (see figure 1)). The spatial distribution of the soot mixing weight (${w}_{{\rm{s}}})$ thus can be obtained, as well as the ${{\rm{AOD}}}_{{\rm{mixture}}}$ and ${{\rm{SSA}}}_{{\rm{mixture}}}.$ The schematic flowchart of the proposed approach in this study is illustrated in figure 2.

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The MODIS sensor, equipped with 36 bands in the visible and thermal infrared spectrum, is a key instrument onboard the NASA Earth Observing System platform, the Terra and Aqua satellite. The Terra satellite passes from north to south across the equator in the morning, while the Aqua satellite passes south to north over the equator in the afternoon. Terra MODIS and Aqua MODIS can provide almost daily global coverage for the investigation of the land, ocean, and atmosphere. Aerosol products from Terra MODIS and Aqua MODIS have been broadly applied to atmospheric research and are known as 'MOD04' and 'MYD04', respectively. The MODIS data and products are utilised for optical property retrievals of polluted dust in this study.

For the remote sensing of aerosol, the cloud screening and surface reflectivity fixing are the two steps before aerosol retrieval is performed. The decision of surface reflectance directly affects the accuracy of aerosol retrievals, hence it is of vital importance. In general, there are two approaches to surface reflectance determination for aerosol products (e.g., MOD04/MYD04): the relationships between spectral surface reflectance and pre-constructing a dataset of global surface reflectance. Because the aerosol effects on the shortwave infrared (SWIR) spectral bands are slight in the TOA surface reflectivity, the surface reflectance of the visible band can be reasonably determined based on the SWIR reflectance (Drury et al 2008). This reflectance correlated well with the visible reflectance over dark areas (i.e., the dark target method). However, the obscure correlation over bright surfaces (high surface reflectance) results in the limitation of this approach. To overcome this limitation, a dataset of global surface reflectance has been pre-constructed based on the minimum reflectivity technique (MRT) of the Deep Blue algorithm, particularly applied to the bright surface in arid and desert areas. Because the source areas of mineral dusts usually exhibit a bright surface, the MRT is consequently employed in the present study. MODIS surface-reflectance products (MOD09) are employed under a clear-sky situation. The criterion of having an AOD_0.550μm smaller than 0.1 is selected for determining surface reflectance according to previous studies (Herman and Celarier 1997, Koelemeijer 2003). Moreover, to mitigate bidirectional reflectance distribution function effects, the observation geometries of the reference image for surface reflectance has been judiciously selected to be as consistent as possible for the target image in this study.

The AERONET joint programme, established by NASA and PHOTONS (PHOtométrie pour le Traitement Opérationnel de Normalisation Satellitaire; University of Lille 1, CNES, and CNRS-INSU), provides a global, long-term, continuous and readily accessible public domain database of aerosol microphysical and radiative properties by means of ground-based measurements. Therefore, aerosol properties from AERONET are not only the best choice for the empirical property of aerosols but also validation of satellite retrievals. Giles et al (2012) have used the long-term AERONET dataset for the optical characteristics of four aerosol categories by grouping up to 19 sites near the source areas of emission, including dust particles, mixed aerosols, urban/industrial pollutants and biomass burning smoke. For the mixed type aerosols, Sede Boker (30.86° N, 34.78° E) and adjacent Cairo (30.08° N, 31.29° E) are the appropriate locations for polluted dust (dust–soot aerosols) observation due to the availability of a complete dataset and because of the dominant aerosol types (Zakey et al 2004, El-Metwally et al 2008). In this study, the empirical/representative light-absorbing property of regional dust particles can be summarised during the dusty days on the basis of the long-term observations of AERONET sites, both for Sede Boker and Cairo (Prasad and Singh 2007, Wang et al 2009). Certainly, Sede Boker is one of the few sites in the world with long-term observations spanning more than 15 years. The long-term measurements have enabled researchers to compile representative statistics in order to evaluate aerosol absorption properties for the proposed approach in this study. The light-absorbing properties of regional dust particles are principally described by the imaginary part of the REFI. In accordance with historical observations, the empirical value of the REFI of 1.55 + 0.003 37i and 1.55 + 0.003 17i at 0.441 μm are suggested for the pure dusts at the Sede Boker and Cairo sites, respectively. For the further applicability on a global scale, the empirical value of the REFI is available as well if long term observation can be provided.

The geographical location of Sede Boker is relatively remote from local pollution sources; however, it lies at the crossroad between downstream dust from the Sahara and the Arabian Peninsula and anthropogenic pollution from Europe and nearby sources (e.g. Cairo city). Similar to the Sede Boker site, the areas around the Cairo site usually receive influence from dust storms that occur from the Sahara Desert. With the local emission of BC from open fires, dust–soot aerosols can be observed often (El-Askary and Kafatos 2008, El-Metwally et al 2008). Two dusty cases for each site were selected to validate the performance of the proposed approach in this study, including the different levels of dust particle loading, mixing weight and surface reflectivity, as shown in the true colour images in the left panels of figure 3. The look-up tables corresponded to the geometry and location of each MODIS image extracted from the constructed database of polluted dust for the case studies are displayed in the right hand side panels of figure 3. For the constructed database of polluted dust, the MODIS TOA reflectance is a function of AOD_mixture and SSA_mixture, as well as the w_s in the look-up table. That is, the properties of polluted dust (AOD, SSA and w_s) can be noted by the location of MODIS TOA reflectance in the τ- and ω- axes of the look-up table, as denoted by the red cross symbols. For the validation of the proposed approach, the values of AOD and SSA from the AERONET dataset and MODIS aerosol products (MOD04/MYD04) are also included in τ- and ω- axes of the look-up tables as the other two symbols demonstrated (black dots and circles).

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The first case shown in figure 3(a) is a dust haze mixed with approximately 8.75% weight of soot aggregates, as suggested by satellite observations over the site location of Sede Boker. For the medium level of soot mixing weight, both retrievals of MOD04 and this study are similar to the ground-based measurements. The second case (figure 3(b)) is a dust haze circumstance as well but has a slight loading of dust particles in contrast to first case. These two cases have almost the same magnitude of AOD (approximately 0.7), but the value of SSA obviously decreased (i.e., from 0.915 to 0.899 based on ground measurements), perhaps due to the mixing effect of soot aggregates. In this case, the result of the mixing weight determination indicated a high-level mixing event (13.75%) with absorbing aerosols (soot-like aerosols) of polluted dust. When compared to the AERONET measurements, the performance of the MODIS aerosol products (MYD04) has an approximately 2.89% overestimation and a 32.96% underestimation in SSA and AOD, respectively, indicating the significance of mixing effects of soot-like aerosols under such circumstances. The similar effect comes up in the third case (c) (see also table 1). It is worth mentioning that the pattern of LUT would vary with a brighter surface (e.g. Sede Boker) under the situations of near nadir observation as figure 3(c) displays.

For the examination of different intensities of dust loading and surface reflectivity in this study, Cairo was selected because the location is frequently on the path of dust storms generated in the Sahara Desert and is often under the influence of heavy anthropogenic pollutants around urban areas. In the third case on 19 February in 2011, dust plumes from the Sahara Desert to the Mediterranean Sea and Nile Delta Region can be clearly observed from the MODIS true colour image shown in figure 3(d). In comparison with MODIS aerosol products, the results of the proposed approach are much improved in the retrievals of AOD and SSA (table 1), indicating the significance of the mixing effect on the retrievals of polluted dust. An obvious dust storm followed the zonal westerlies and passed through the greater Cairo Region; this event is the case study for pure dusts as shown in the image in figure 3(e). The blowing dust plumes might display as 'pure dust' under the circumstances of such a strong storm. According to the multi-spectral MODIS TOA reflectance, the soot mixing weight of dust particles is close to 0.3% at Cairo site, as suggested by the proposed approach, indicating the 'pure dust' status when a satellite passes over. The in situ measurement of AERONET also exhibited the same result, supporting the efficient dust model employed in this study.

Meanwhile, MOD04/MYD04 retrievals exhibited the obvious difference from ground measurements in this dust storm event (pure dust case). The noticeable difference may be caused by the properties used in the dust model (REFI and size parameter) and the coarse spatial resolution (10 km × 10 km) of MOD04/MYD04 products with respect to the point measurement of AERONET. As we know, the dust plumes usually exhibit a discontinuous spatial distribution and then result in a large deviation of TOA reflectance from the MODIS sensor within such a coarse area. Thus the retrievals could be diverse depending on the variance in TOA reflectance. Moreover, surface inhomogeneity with dark areas of the Nile Delta adjacent to the bright surface of Cairo city could be the other factor causing the dissimilarity between MOD04/MYD04 and AERONET measurements. Certainly, the Deep Blue algorithm assumes no absorption at 0.670 μm (i.e., SSA_0.670μm = 1.0) for pure dusts, and this assumption could be the potential cause of the obvious difference in this case. In fact, the different absorption would cause the variance in SSA of dust particles. For example, 2.6% of the variations in SSA might result in 13.1% variance in the TOA reflectance simulation at 0.650 μm on a bright surface and then further underestimate the MOD04/MYD04 AOD retrievals (Lin et al 2013). Therefore, the determination of the empirical absorption (REFI) is significant in retrieving the properties of polluted dusts, as the last case shown at Sede Boker on 21 March 2012 of this study indicates (figure 3(f)). The difference of the SSA retrieval in this study (0.905) from the AERONET measurement (0.873) is evident even as the AOD retrieval is consistent. In review of the MODIS true colour image, the dust plumes were apparently transported from the Arabian Peninsula, potentially exhibiting a different REFI from the counterpart of Sahara dusts used in this case. The result illustrates the essential nature of dust property employed in the mixing weight determination of polluted dusts.

Table 1 displays the summary of the case studies in figure 3. The overall comparison presents the improvement of using the proposed approach in reducing the errors from 32.95% to 6.56% of AOD and from 2.67% to 0.83% of SSA retrievals on average, and reasonably providing the soot-like mixing weight for the polluted dusts. The comparisons between ground-based measurements (AERONET) and MODIS aerosol products (MOD04/MYD04) can be clearly found from figure 4. On the other hand, the results also suggest that the higher spatial resolution (1 km × 1 km) could benefit both the accuracy and spatial distribution in the process of retrieving optical properties of polluted dusts.

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Because the case studies show that the soot mixing weight plays the key role in the aerosol retrievals (AOD and SSA), the determination of mixing weight for polluted dust is thus essential, especially over the areas where ground measurement (i.e., AERONET) is absent. Taking the area of the Nile Delta as an example (figure 3(d)), the determination of soot mixing weights and the spatial distribution of polluted dust can be demonstrated in figures 5(a) and (b). The spatial distribution of mixing weight clearly describes the situation of Saharan dusts driven by the westerlies circulation into northwestern Africa, as the MODIS true colour image shown in figure 3(d). Thus, the spatial properties of polluted dust, AOD_mixture and SSA_mixture can be accurately retrieved in accordance to the corresponding weight of mixing soot (see also figures 5(c) and (d)). Figure 5(a) shows, that the soot mixing weight dispensed in the test area (5 km × 5 km) displays a noticeable variation, approximately 10.0% to 15.0%, indicating the potential uncertainty of aerosol retrievals could be induced under the assumption of uniform spatial distribution. In this case, the uncertainty of ${\mathrm{AOD}}_{\mathrm{mixture}}$ and ${\mathrm{SSA}}_{\mathrm{mixture}}$ retrievals is approximately 10.0% and 1.4%, respectively.

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