Satellite Retrievals of Aerosol Optical Depth over a Subtropical Urban Area: The Role of Stratification and Surface Reflectance

We explore the relationship between satellite retrievals of aerosol optical depth (AOD) and surface aerosol mass concentrations over a subtropical urban area, namely, Santiago, Chile (33.5°S, 70.6°W, 500 m.a.s.l.). We compare 11 years of AOD from the MODerate resolution Imaging Spectroradiometer (MODIS) with in situ particulate matter mass concentrations (PM). MODIS AOD reaches its maximum in summer and minimum in winter, the opposite of the annual cycle of surface PM. To improve our understanding of the relevant governing processes, we use a simple model that estimates the boundary layer (BL) AOD based on measured PM, relative humidity and BL height (BLH) as well as best estimates of aerosol composition, size distribution, and optical properties. Model results indicate that a weak annual AOD cycle is due to the opposite annual cycles in BLH and PM, which is largely supported by the Aerosol Robotic NETwork (AERONET) data collected in 2001 and 2002 in Santiago. We identify a possible bias linked to the operational estimate of surface reflectance that may lead to a spurious summer maximum in MODIS AOD over Santiago. This misfit in surface reflectance appears to affect not only Santiago but also a significant area of the semi-arid Southern South America. Sensitivity experiments with the simple model indicate an underestimate of simulated AOD as compared to AERONET data. This underestimate points to the possible role of residual aerosol layers in the AOD measured at the surface (not included in the simple model). Cirrus clouds appear not to play a significant role in explaining the MODIS AOD seasonality. The need for improved characterizations of aerosol properties and their temporal and spatial distribution in cities such as Santiago is emphasized.


INTRODUCTION
Air quality is an issue of concern in many South American cities, and substantial efforts have been made by local authorities to measure so-called criteria pollutants (Gallardo et al., 2012a and references therein).However, aerosol measurements in the region are still sparse and usually limited to mass concentrations of partially (PM 10 ) and completely (PM 2.5 ) inhalable particles, which hampers their usefulness as tools for improved understanding of impacts on health, ecosystems and climate, and for the actual evaluation and design of curbing policies.Thus, it is appealing to use remote sensing to supplement existing ground measurements where available or to infer ground concentrations of particles where absent.In fact, if at a given location urban aerosols are the dominant source of atmospheric turbidity, one would expect to find a relationship between aerosol optical depth (AOD or τ) and particulate matter (PM), as reported for many locations (e.g., Engel-Cox et al., 2004;Pelletier et al., 2007;Schaap et al., 2009;Boyouk et al., 2010;Tsai et al., 2011;Estellés et al., 2012).However, such a relationship is modulated by local emissions and meteorological conditions, as well as by the assumptions underlying the retrieval of AOD (e.g., Song et al., 2009).Therefore, validation studies of remotely sensed AOD should consider local conditions and expertise, and provide an explanation of the AOD-PM relationship based on physical principles.
One of the space-borne instruments that acquire AOD is the MODerate resolution Imaging Spectroradiometer (MODIS), which is a 36-band spectrometer widely used by the research community (Kaufman et al., 1997;Remer et al., 2005;Levy et al., 2007a, b;Levy et al., 2009).MODIS AOD has been validated against ground-based AOD measurements collected by the Aerosol Robotic NETwork (AERONET, Holben et al., 1998) for different atmospheric conditions and different locations with encouraging results (e.g., Levy et al., 2010;Bréon et al., 2011;Hyer et al., 2011;Mei et al., 2012).
The MODIS retrieval algorithm for AOD considers assumptions regarding surface reflectance, aerosol properties, etc. (Levy et al., 2007a, b).In particular, surface reflectance estimates are crucial in the AOD retrievals in the case of low aerosol loading over land (τ ≲ 0.15) (Levy et al., 2010).Recently improved methods for the treatment of surface reflectance have been proposed.For example, He et al. (2012) and Guang et al. (2012) use a Bidirectional Reflectance Distribution Function (BRDF) model to calculate both the surface reflectance and the MODIS AOD simultaneously.An analysis of the MODIS AOD algorithm sensitivity to the surface reflectance assumptions is presented by Mielonen et al. (2011), and modifications to the surface reflectance parameterization of the MODIS AOD algorithm are proposed by Oo et al. (2010) and Mielonen et al. (2011).Also, it has been shown that the MODIS algorithm is sensitive to thin cirrus contamination (Gao et al., 2002;Roskovensky and Liou, 2005).Moreover, Drury et al. (2008), Drury et al. (2010), andSchwartz et al. (2012) have reported difficulties in MODIS AOD over arid and semi-arid region in the southwestern United States due to a bias in MODIS AOD linked to inaccurate estimations of surface reflectance.In summary, surface reflectance is a key parameter, subject to uncertainties, that must be carefully evaluated to establish the relationship between AOD and PM, particularly over arid and semi-arid zones.Hoelzemann et al. (2009) presented a multiyear comparison for South America between groundbased AERONET AOD observations and the MODIS AOD satellite product.This analysis excluded stations in Southern South America (SSA) where only a few places have sunphotometer records for more than two years and therefore compromise the adequate validation of any spaceborne instruments that acquire AOD (MODIS in particular) over SSA.
We attempt to investigate the applicability of MODIS AOD to assess the aerosol loading in the boundary layer for Santiago de Chile (33.5°S 70.6°W, 500 m.a.s.l),where health concerns (e.g., Valdés et al., 2012) and potentially cloud and climate impacts (e.g., Saide et al., 2012) require an improved characterization of atmospheric particulates.Moreover, we chose Santiago because it is located under the prevailing subsiding regime imposed by the South Eastern Pacific anticyclone, which contributes to both a well-defined and very stable boundary layer (e.g., Muñoz and Undurraga, 2010;Saide et al., 2011), and a large number of clear days for successful AOD retrievals.Given the heavy load of particulates over Santiago and the absence of frequent visible aerosol layers above the boundary layer, we expected to find a direct relationship between AOD and PM.However, when comparing 11 years of MODIS AOD and concurrent PM surface concentrations, we found that MODIS AOD is at a maximum in summer and minimum in winter, as opposed to the annual cycle of surface PM, shown in Figs.1(a In order to improve our understanding of the relevant governing processes behind the aforementioned AOD-PM relationship, we implemented a simple model that estimates the boundary layer (BL) AOD based on measured PM, relative humidity, and BL height (BLH), as well as best estimates for aerosol composition, size distribution, and optical properties.This simple model was subsequently applied to describe the diurnal variability of AOD, testing simple model results against sunphotometer data collected during a short campaign, and against available AERONET data.Above all, this study explores the physical basis of the AOD-PM relationship, and identifies the potential cause for inconsistency between MODIS and AERONET measurements not only over Santiago, but also possibly over other subtropical areas.We expect that this study can trigger more thorough exploration of boundary layer and aerosol processes in Santiago, based on improved observational platforms that integrate satellite and ground based measurements.
In the following paragraphs we present the data used in this study.The simple model is described thereafter.Results and discussion will follow the model description, and we will close with summary and conclusions.

DATA
Hourly records of particulate matter with aerodynamic diameter less than 10 µm (PM 10 ) and less than 2.5 µm (PM 2.5 ) at four stations in Santiago are available from the Ministry of Environment for the 2000-2010 period (http://sinca.mma.gob.cl/).In this study, we used hourly averages of PM 10 and PM 2.5 mass concentrations from the Parque O'Higgins station located in downtown Santiago (Fig. 2).For one day in the winter of 2011, we also looked at 5-minute averages of PM 10 and PM 2.5 mass concentrations at Parque O'Higgins.We chose this station because it is located in a park in a flat area and reflects average conditions of the basin as shown by Osses et al. (2013).They introduced a "representativity" index for a given station that is linked, on the one hand, to the precision of the measurements, and, on the other hand, to the magnitude of the measurements.With respect to the Osses et al. (2013) "representativity" index, Parque O'Higgins is a good proxy for average PM conditions in Santiago, confirming the assumption made previously by various authors (e.g., Gallardo et al., 2012a and references therein) of using Parque O'Higgins as a representative site for the average air quality in Santiago.
Composition and, more rarely, size distribution have been assessed sporadically for aerosols in Santiago in connection with short-term campaigns (e.g., Morata et al., 2008;Gramsch et al., 2009).In this study, we used the aerosol composition reported in the latest version of the Attainment Plan for Santiago (PPDA, 2010), which refers to a composition analysis of particulates in Santiago for 2005 which, to the best of our knowledge, has not been published in the scientific literature.The composition adopted here is shown in Table 1.Very recently, Carbone et al. (2013) reported results from a few months' record of aerosol composition using an Aerosol Chemical Speciation Monitor.These data suggest a larger fraction of organic aerosols than the one considered in PPDA ( 2010).Nevertheless, lacking a better characterization of the optical  properties, particularly of organic aerosols, we used the 2010 partitioning assuming that all carbonaceous aerosols are as absorbing as black carbon.With lack of better data, aerosol refractive indexes and densities were taken from the literature, except for the density of dust.Morata et al. (2008) provided a mineralogical analysis of collected aerosols in Santiago with aerodynamic diameter > 2 µm.These particles can be associated with the dust category in Table 1 (Valdés, 2011).Dust density was estimated by weighting each mineral according to the speciation referred to by Morata et al. (2008).
In the early 1990's in Santiago, Horvath and Trier (1993) and Trier and Horvath (1993), reported bulk aerosol extinction coefficients in the range 0.1 to 1, Ångström exponent (~1.22) and aerosol mass extinction coefficients (~5 m 2 ⁄g).However, emission patterns in Santiago have changed significantly since this period (e.g., Gallardo et al., 2012b) and, lacking recent data and instead of using results from Horvath and Trier (1993), we use AOD derived from the AERONET record collected in Santiago from August 2001 to October 2002 to compare with our simple model AOD simulations (This model is described later in the paper).The AERONET data set contains ~7800 AOD measurements of Level 2 data and 53 inversions (Dubovik and King, 2000) for aerosol properties (e.g., size distribution, phase function, single scattering albedo) over Santiago.These inversions have an average asymmetry parameter of 0.7 for a 441-nm wavelength and 0.63 for a 675-nm wavelength, with standard deviations of 0.03 and 0.04, respectively.The average Ångström exponent of all measurements between 440 and 675-nm was, 1.3 with a standard deviation of 0.4.Single scattering albedo (ω) was calculated for 10 inversions, resulting in ω ~0.91 at visible wavelengths (standard deviation ~0.05).Both ω and the asymmetry parameters were not used in the model simulation, and they are presented only to note the similarity of the AERONET-derived aerosol optical properties to those used in the moderately absorbing model by the MODIS land algorithm.
Aerosol, land, and cloud products are available from the MODIS Atmosphere group website (http://modis-atmos. gsfc.nasa.gov).Terra and Aqua are polar orbiting satellites with approximate local pass times (UTC-4) of 10:30 and 14:30, respectively, over Santiago.Since BLH data are available for the morning hours as described in Muñoz and Undurraga (2010), we use data collected from the Terra satellite only.Nevertheless, the seasonal behavior of AOD is similar for both platforms over Santiago (not shown).Aerosol products correspond to MOD04 level 2, Collection 5.1.The reliability of the MOD04 product is expressed by a Quality Assurance Confidence (QAC) flag, which varies between 0 ("no confidence") to 3 ("very good confidence") (e.g., Levy et al., 2009;Hubanks et al., 2012).We adopted the recommendation of the MODIS team and used QAC = 3 (Levy et al., 2009), which corresponds to 17% of the pixels over Santiago.Deep Blue products (Hsu et al., 2004(Hsu et al., , 2006) ) could not be used since 99% of the pixels over Santiago presented QAC flag in the "marginal" or "no confidence" categories.Due to the complex topography surrounding Santiago, we considered a 25 km by 25 km square over the city (Fig. 2) and each daily value of MODIS was calculated as an average of all pixels with QAC = 3 in the 25 km by 25 km square.
Additional sunphotometer data were collected on July 22, 2011 using a Microtops II sunphotometer at the Center for Mathematical Modeling (CMM) building within the Faculty for Physical and Mathematical Science (FCFM, from the Spanish acronym of Facultad de Ciencias Físicas y Matemáticas), University of Chile (Fig. 2).
We took cloud properties retrievals from the MODATML2 Joint Atmosphere products (http://modis-atmos.gsfc.nasa.gov).The MOD43B1 product (Schaaf et al., 2002), which includes the Bidirectional Reflectance Distribution Function (BRDF) model parameters, was used to estimate the surface reflectance in the selected pixels of MOD04.Additionally, we considered cloud observations taken regularly at the Santiago international airport (Fig. 2) by the Chilean Weather Office.This data set includes type of observed cloud, cloud height, and cloud cover in octas.
On the roof of the Department of Geophysics (DGF) at the FCFM in downtown Santiago (Fig. 2), a complete meteorological station and a ceilometer (CL31 Väisälä) have been operational since 2007, allowing a climatology of the BLH (Muñoz and Undurraga, 2010), as well as an indication of aerosol loading (Muñoz and Alcafuz, 2012).These data are used in the simple model described in the next section.

SIMPLE AEROSOL OPTICAL DEPTH MODEL
For simplicity´s sake, we consider an externally mixed aerosol model.Total AOD is the sum of contributions of each aerosol type, which is based on a model shown by Seinfeld and Pandis (2006) where j identifies each aerosol composition in Table 1; BLH is the boundary layer height; D p is the particle diameter; D p max is maximum the particle diameter to be considered in the integration; Q ext (m,RH,λ,D p ) is the extinction efficiency; m is the complex refractive index; λ is the wavelength considered; n j (D p , RH, PM 2.5 , PM 10 ) is the aerosol number size distribution; RH is the relative humidity.
Dust aerosol number size distribution corresponds to a rural distribution taken from Jaenicke (1993); ammonium nitrate and ammonium sulfate distributions are based on those described by Plaza et al. (2011), and the black carbon distribution is a unimodal distribution based on measurements by Gramsch et al. (2009).These distributions are numerically represented by more than 40 size bins, and to take into account PM mass concentration observations, these above presented a priori distributions are scaled according to the PM 10 and PM 2.5 values such that where PM 10j and PM 2.5j are mass concentration of the aerosol type j of Table 1.PM 10j and PM 2.5j values are calculated as the product between the PM 10 (or PM 2.5 ) mass concentration, and the "PM mass" factor shown in Table 1 (e.g., if PM 2.5 = 40 [µg/m 3 ], then PM 2.5Black Carbon = 40 × 0.5 = 20 [µg/m 3 ]).Also, in Eqs. ( 2) and (3), n mj (•) is the mass distribution for composition j, calculated on the basis of the number distribution and assuming spherical and constant density particles.The density of the particles depends on the density of the aerosol (Table 1) and is adjusted using density changes due to water uptake for the hydrophilic particles -in this model, ammonium nitrate and sulfate.Hygroscopicity of ammonium nitrate and ammonium sulfate are taken from Gong et al. (2003) and the refractive indexes for the hydrophilic particles are calculated using a simple volume mixing rule as described by Levoni et al. (1997).Extinction efficiency is calculated for each aerosolbin using a Mie scattering calculation code provided by Mätzler (2002).
Lacking a vertical profile for the PM, we assume a wellmixed aerosol profile between the surface and the top of the boundary layer.BLH data are multi-year averages obtained from Muñoz and Undurraga (2010) and adjusted by a simple parameterization of the BLH diurnal cycle.As in the July 22 nd case we had ceilometer data, we take advantage of these data assuming a linear relationship between the ceilometer backscattering reflectance and the PM 10 concentration from the surface to the top of the boundary layer (Muñoz and Alcafuz, 2012).

RESULTS
In this section we show, on the one hand, the ability of our simple model to capture the variability in AOD inferred from sunphotometer measurements.On the other hand, we explore the relationship between MODIS AOD and PM mass concentrations in the boundary layer.

Model Results and Their Validation
Given the many assumptions and uncertainties involved in our simple AOD-PM model, we evaluate its ability to capture the seasonal and diurnal AOD variability.First we examine the ability to capture seasonal variations against available AERONET AOD.In order to verify model runs, we further explore the diurnal variability in AOD by comparing model outputs with AOD data collected by sunphotometer in 2011.Both comparisons also show the model´s sensitivity, respecting the prescribed particle composition and density.
In Fig. 3, seasonal variation of the available AERONET AOD for Santiago (for ca.one year starting in August 2001) at 500-nm wavelength is compared with the model output for our best guess of aerosol composition and density as provided in Table 1.We calculate upper and lower limits for our model outputs considering a range of possible composition and density values.The sensitivity analysis is made with respect to a) variations in particle density, for which we assume ± 25% around the best estimate value, and b) different aerosol compositions, including pure dust, pure ammonium sulfate, pure ammonium nitrate and pure black carbon aerosol.The lower bound of our estimates corresponds to simulations with pure dust and high particle density parameters, while the upper bound corresponds to pure black carbon and low particle density.The exploratory campaign carried out using a Microtops II instrument on the roof of the CMM allows a preliminary evaluation the model with respect to diurnal variations (Fig. 4).No clouds were observed during that day.Evolution of the diurnal BL presents an interesting structure, as shown by the reflectivity of the ceilometer.PM 2.5 shows a maximum around 12:00 local time, whereas the maximum in AOD occurs two hours later and coincides with a steep increase in BLH from 150-200 m to 350-400 m.Simulated AOD shows a systematic underestimate (~33%), but it captures the variability of the measurements (correlation coefficient ~0.96) in response to the PM vertical profile derived from the ceilometer reflectivity and the PM surface concentration.
In summary, we find that model results show seasonal and single day diurnal variability comparable with that shown in available sunphotometer measurements of AOD.However, a systematic underestimate of simulated AOD values is apparent.Factors such as the existence of internally mixed aerosols (e.g., Jacobson, 2001), non-spherical particles (e.g., Wang et al., 2013) or the presence of upper aerosol layers or residual layers (e.g., Seguel et al., 2013) might help explain model underestimation with respect to observations.The study by Seguel et al. (2013) showed near surface ozone origin measured in the residual layer by ozonesondes that accumulates between the top of the mixed layer and the base of the subsidence inversion.Additionally, data from an elastic Light Detection and Ranging system, and a ceilometer over Santiago show unequivocal layers of aerosols above the mixed boundary layer (Muñoz and Alcafuz, 2012).The presence of residual aerosol layers may explain the simple model underestimate of AOD.The contribution of these residual layers of aerosols to total AOD remains as a future question.Despite these shortcomings, we deem the model reliable enough to address seasonal and diurnal variability in AOD.Of course, a more thorough evaluation of the seasonal and diurnal variations in AOD will require more detailed and accurate observations, in particular, systematic and long-term AOD observations over Santiago are required.

MODIS AOD vs. PM Mass Concentrations
Monthly means of MODIS Terra 550-nm AOD retrieval and in situ PM 2.5 mass concentration measurements at MODIS Terra pass time over Santiago are shown in Fig. 5.Over Santiago, PM 2.5 concentrations show a strong winter maximum, while MODIS AOD shows a distinct minimum.The depth of the convective boundary layer (BLH) has a strong seasonality at Terra satellite pass time, with ~550 m in summer and ~130 m in winter (Fig. 5).The opposite cycles in BLH (higher in summer and lower in winter) and PM 2.5 mass concentration (higher in winter and lower in summer) lead to a weak seasonal cycle in the PM burden in our model (not shown).This would result in the weak seasonal cycle of AOD in our model, which is in disagreement to that of MODIS AOD (Fig. 5).To explain this mismatch, we shall check the effects of cirrus contamination and surface reflectance, which seasonal cycles were not considered in our simple model.
To elucidate the effects of cirrus contamination (Gao et al., 2002), we use MODIS cloud related products to check that the pixels used in these comparisons were in fact clear sky in terms of cloud optical depth, cirrus reflectance, and cloud cover fraction.Days with good quality MODIS retrievals were mostly clear-sky (80% clear, 95% partly cloudy with cloud fraction ≤ 0.1; cirrus reflectance < 0.01 in the 99% of the data).Human observers report cloud data at the airport that also corroborate the absence of clouds for most of the MODIS good quality retrievals (72% clear, 85% partly cloudy with cloud fraction ≤ 0.1).One should recognize that human observers might register clouds that are outside the selected satellite pixels over Santiago, and  these clouds registered by observers might not affect the MODIS retrieval.Also, according to the observers' report, cirrus frequency peaks in spring.Cirrus seasonality is not in phase with the MODIS AOD seasonality, and therefore it can be concluded that cirrus does not explain the MODIS AOD summer maximum.
As stated earlier, surface reflectance is also an important parameter in the MODIS AOD retrieval algorithm.Moreover, MODIS AOD retrievals over places with low AOD (τ < 0.15) are especially sensitive to estimations of surface reflectance (Levy et al., 2010).Santiago is a site with relatively low AOD (Fig. 3) for which an accurate estimate of surface reflectance could be a crucial parameter in MODIS AOD retrieval.The algorithm for MODIS AOD retrieval chooses the best combination of Fine Mode Fraction (η), AOD and surface reflectance such that the difference between observed MODIS reflectance and model-calculated reflectance in the 0.66-µm wavelength is minimized, subject to the constraint that the modeled and observed reflectances in the 0.47 an 2.12-µm channels are equal (Levy et al., 2007a, b;Levy et al., 2009).In order to check the surface reflectance calculations in the aerosol algorithm, we use the combined Terra-Aqua BRDF/albedo level 3 product MCD43 as our surface reflectance guide.The MCD43B1 product includes the parameters of the BRDF model.Reprojecting these data onto a MOD04 grid and using the BRDF algorithm from the Boston University MODIS group (http://www-modis.bu.edu/brdf), we simulate surface reflectance as viewed from the satellite on each pass (Fig. 6).The MODIS AOD operational algorithm has no discernible seasonal variation in surface reflectance, whereas the BRDF derived product does show a marked seasonal variation in surface reflectance, with higher values in summer (December, January and February).Therefore, the difference between the two surface reflectances presents a seasonal pattern, as do the AOD retrievals (Fig. 6(b)).If we consider surface reflectance from BRDF to be more accurate than surface reflectance from the aerosol algorithm, this difference should be an important source of error when retrieving AOD for Santiago.Moreover, the ratio between 660 nm and 2130 nm BRDF derived surface reflectance (mean of ~0.68 with standard deviation of 0.03) is considerably higher than the MOD04 surface reflectance ratio (mean of ~0.5 with standard deviation of 0.02).Similar differences in the 660/2130 nm ratio of surface reflectance in an urban context have been found by Oo et al. (2010) who compare the surface reflectance 600/2130 ratio of the MOD04 algorithm with the one derived from a high spectral resolution Hyperion dataset (Datt et al., 2003).
Finally, aerosol types treated differently would have resulted in the introduction of some biases to AOD.The MOD04 algorithm regards all the pixels analyzed as sulfate aerosol, which is different from the composition reported in Table 1 as well as from the few AERONET inversions that suggest moderately absorbing aerosols.On the other hand, according to the algorithm, 99% of the pixels are tagged as pure coarse mode (η = 0).This is also different from the mass concentration measurements ratio (PM 2.5 /PM 10 ≃ 0.47) and/or the η m = τ f /(τ f +τ c ) ≃ 0.8 indicated by our model, where τ f and τ c are the contributions of the fine (PM 2.5 ) and coarse (PM 10-2.5 ) aerosols to AOD in the model.The positive difference between real and calculated surface reflectance would lead the algorithm to choose a coarse dust model as the appropriate aerosol model during the minimization of the 0.66-µm channel (Mielonen et al., 2011).Consequently, the surface reflectance products derived from the BRDF and the MOD04 suggest an underestimation of both the magnitude of the surface reflectance at 0.66 µm and the ratio between 660 and 2130 nm surface reflectance.These underestimations lead to the MODIS operational algorithm's election of non-absorbing coarse aerosols over Santiago (e.g., Mielonen et al., 2011), which in turn may result in an overestimate of AOD, particularly in summer when the difference between MOD04 and BRDF surface reflectance estimates is largest.
Other regions in South America could show similar patterns in seasonal differences between the two estimates of surface reflectance and could present similar seasonal behavior in the MODIS AOD retrieval.Maps of seasonal differences between the two estimates of the surface reflectance can be a useful tool to identify these regions, as illustrated in Fig. 7.The amplitude of the seasonal cycle in MODIS AOD, shown in Fig. 7(c), is consistent with the magnitude of the seasonal cycle of the reflectance difference between the two MODIS products (in Fig. 7(f)), especially in the semi-arid Patagonian region in the SSA.A further confirmation that surface reflectance might also be the source of a spurious seasonality is given by AERONET data taken at Trelew (43.3°S,65.3°W,15 m.a.s.l).At this site, MODIS AOD shows a summer maximum not observed in the AERONET AOD data (shown in supplementary material).Other cities in SSA that present small differences in the magnitude of surface reflectance, such as Córdoba (31.4°S, 64.2°W) and Buenos Aires (34.6°S, 58.4°W), do not show significant differences in the comparison between MODIS AOD and AERONET AOD seasonality (not shown).Hence, combined evidence strengthens the idea that the MODIS AOD seasonality over Santiago is spuriously driven by the operational estimate of surface reflectance.

SUMMARY AND CONCLUSIONS
In this study, we explored the relationship between MODIS AOD and PM mass concentration over a subtropical urban area in the Southern Hemisphere, namely Santiago de Chile.We applied a simple, semi-empirical AOD-PM model that captures both the diurnal and seasonal variability in AOD according to available sunphotometer measurements.Model results suggest both a weak seasonal variability of AOD over Santiago due to opposite variations in boundary layer height and aerosol mass concentrations and a similar contribution of the PM 2.5 and BLH variability to the AOD calculation in both diurnal and seasonal time scales.On the other hand, MODIS AOD demonstrates considerable amplitude of the seasonal cycle (~50% below the annual mean in winter and ~20% above the annual mean in summer).Our analysis suggests that cirrus clouds are not the primary reason for the inconsistent seasonality between the MODIS AOD and the simulated AOD.By comparing surface reflectances derived from the operational aerosol algorithm and from the BRDF product, we find that summer reflectances are considerably lower than expected in an urban setting, possibly leading to an overestimate of aerosol AOD.A similar bias in surface reflectance is found over other semi-arid areas of SSA.The simple model suggests that up to one third of the AOD could be attributed to the presence of residual aerosol layers over the estimated BLH.The impact of aerosols within the residual layers in AOD seasonality in both model and observations remains to be quantified.
Our results suggest that the MODIS AOD retrieval algorithm requires an improved estimate of surface reflectance, particularly in summer and over vast semi-arid areas of SSA, and possibly over other arid and semi-arid regions (e.g., Drury et al., 2008).The potential bias in MODIS AOD discussed here over large arid or semi-arid regions could introduce spurious values of AOD in assimilation experiments and potentially affect the determination of aerosol sources, radiative forcing, and air quality calculations (e.g., Huneeus et al., 2012;Saide et al., 2012;Schwartz et al., 2012) Evidently, there is a need for further validation of satellite borne instruments against in situ measurements and sunphotometers over SSA.Specifically, we expect to reestablish Santiago as an AERONET site.To advance in the quantification of radiative and health related impacts of aerosols over large urban centers in South America will require quality controlled and regular measurements of aerosol composition, size distribution, and optical properties.In the case of Santiago where boundary layer processes play such a key role and the presence of not yet characterized residual layers is unequivocal, in situ vertical profiling capabilities must be substantially improved.
) and 1(b).This unexpectedly different seasonality should be interpreted only qualitatively since ground-based AOD measurements by an AERONET sunphotometer that are coincident with MODIS (78 days between 2001 and 2002, mostly in summertime) show a systematic upward bias of the MODIS AOD with respect to AERONET AOD, if AERONET data are considered as "truth" (See Fig. 1(c)).

Fig. 1 .
Fig. 1.Time series of MODIS AOD successful retrievals over Santiago (a) and PM 2.5 hourly measurements in Parque O'Higgins, in downtown Santiago (b), and scatter plot of concurrent MODIS AOD and AERONET AOD (c).The AERONET AOD in panel (c) were calculated using the average of level 2 AERONET AOD over a ± 30 minute window around MODIS pass time and only if 3 or more successful retrievals in the ± 30 minute window were available.For comparison with MODIS AOD, AERONET AOD at 0.55-µm was computed by linear interpolation between 0.5-µm and 0.675-µm on a log-log plot, based on Ångström power law.

Fig. 2 .
Fig. 2. Santiago de Chile urban area and topography.Measurement sites considered in this study are indicated.The black continuous line in (a) represents the urban area, the dotted rectangle is the 25 km by 25 km square considered for MODIS data.Gray-scale regions, thin gray lines and numbers indicate height above sea level in meters.A detail of the small square is shown in (b).The map data were obtained from http://www.openstreetmap.org.
Fig. 3. Monthly means of simulated 500-nm AOD with parameters in Table 1 at AERONET measurement time (gray dotted line) and AERONET 500-nm AOD (black solid line).The bars in (b) represent the total number of AERONET measurements used for each month, and the error bars in (a) the standard deviation.The shaded area around model values represents the sensitivity simulation results at AERONET measurement time (see text for details).
numerous AERONET measurements (September to March) present systematic underestimates, compared to the AERONET AOD.

Fig. 5 .
Fig. 5. Panel (a) shows simulated 550-nm AOD at MODIS Terra pass time (gray line) and MODIS Terra 550-nm AOD (black line) monthly means over Santiago.The shaded area represents the extent of the sensitivity simulations at MODIS Terra pass time.The error bars represent standard deviation.Panel (b) presents monthly means of boundary layer height (black line) and PM 2.5 surface concentration (gray line).Panel (c) shows the total number of MODIS measurements for each month over the entire 2000-2010 period.

Fig. 7 .
Fig. 7. MODIS derived AOD and differences of between surface reflectance estimates for the MOD04 and the MCD43B1 surface reflectance products for the year 2007.Panel (a) MOD04 AOD in summer, (b): MOD04 AOD in winter, (c): difference between MOD04 AOD in summer and MOD04 AOD in winter, (d): difference between MCD43B1 surface reflectance and MOD04 derived surface reflectance in summer, (e): difference between MCD43B1 surface reflectance and MOD04 derived surface reflectance in winter, (f): difference between panels (d) and (e).The blank regions represent no data.The AOD and surface reflectance are derived from the same data set and using the same data processing as for Santiago MODIS AOD and surface reflectance calculations.

Table 1 .
Aerosol composition used in the simple model based on PPDA (2010).Percentages are in terms of total PM 10-2.5 or PM 2.5 for each measurement.Complex refractive index (m) and particle density (ρ) are also shown.