Retrieval of Aerosol Optical Depth over Land Surfaces from Avhrr Data

The Advanced Very High Resolution Radiometer (AVHRR) provides a global, long-term, consistent time series of radiance data in several wavebands which are used for the retrieval of surface spectral reflectance, albedo and surface temperature. Long-term time series of such data products are necessary for studies addressing climate change, sea ice distribution and movement, and ice sheet coastal configuration. AVHRR radiances have also been used to retrieve aerosol properties over ocean and land surfaces. However, the retrieval of aerosol over land is challenging because of the limited information content in the data which renders the inversion problem ill defined. Solving the radiative transfer equations requires additional information to reduce the number of unknowns. In this contribution we utilise an empirical linear relationship between the surface reflectances in the AVHRR channels at wavelengths of 3.75 µm and 2.1 µm, which has been identified in the Moderate Resolution Imaging Spectroradiometer (MODIS) data. Following the MODIS dark target approach, this relationship is used to obtain the surface reflectance at 0.64 µm. The comparison of the estimated surface reflectances with MODIS reflectance products (MOD09) shows a strong correlation. Once this was established, the MODIS " dark-target " aerosol retrieval method was adapted to AVHRR data. A simplified look-up table (LUT) method, adopted from the Bre-men AErosol Retrieval (BAER) algorithm, was used in the retrieval. The aerosol optical depth (AOD) values retrieved from AVHRR with this method compare favourably with ground-based measurements, with 71.8 % of the points located within ±(0.1 + 0.15τ) (τ is the AOD) of the identity line. This method can be easily applied to other satellite instruments which do not have a 2.1 µm channel, such as those currently planned to be used on geostationary satellites.


Introduction
Algorithms developed to retrieve aerosol properties from satellite-based passive instruments, such as radiometers, make optimum use of the information available in the radiation measured at the top of the atmosphere (TOA).The TOA radiation consists of backscattered and reflected upwelling radiation, ideally at different wavebands, multiple viewing angles and/or with polarisation information.The results further depend on the swath width, spatial and temporal resolution.An overview of aerosol retrieval algorithms and products is provided in Kokhanovsky and de Leeuw (2009), de Leeuw et al. (2011) and Mei et al. (2012).Aerosol retrieval is usually only done for cloud-free situations.If that has been verified, for example, by application of a cloud mask, the next important step in the retrieval of aerosol properties from TOA radiances (or reflectances) is the decoupling of the contributions from the surface and from atmospheric constituents.This can be achieved in several ways, Published by Copernicus Publications on behalf of the European Geosciences Union.depending on the instrument characteristics and in particular the number of viewing angles.For single-view instruments, such as MODIS, MERIS, SeaWiFS or AVHRR, assumptions need to be made on the surface reflectance.For instance, the "dark-target" approach developed for the retrieval of aerosol properties from MODIS data uses the 2.1 µm band to estimate the reflectance for visible bands (Kaufman et al., 1997).The 2.1 µm band is used because at this wavelength the effect of aerosol particles on the TOA reflectance is negligibly low (except for coarse mode particles such as for desert dust or sea spray aerosol).Then the relation is sought between the surface reflectances at 2.1 µm and visible wavelengths.Similarly, Holzer-Popp et al. (2009) developed a regression function between the TOA reflectance at 1.6 µm and the surface reflectance at 0.67 µm and von Hoyningen-Huene et al. (2009) use the empirical relationship between 0.67 µm and 2.1 µm bands for sun glint correction for the multi-spectral imager (MSI) instrument.The Bremen AErosol Retrieval (BAER) algorithm for MERIS (von Hoyningen-Huene et al., 2003, 2011) utilises the the normalised difference vegetation index (NDVI).For bright surfaces, the deep blue approach has been developed for MODIS (Hsu et al., 2004) and SeaWiFS (Sayer et al., 2012;Hsu et al., 2013).In the most recent MODIS Collection 6 data set, the dark target and deep blue results have been combined.Some dual-view algorithms such as the AATSR dual-view (ADV) algorithm (Curier et al., 2009;Grey et al., 2006), the multiobservation approach for MODIS (Tang et al., 2005;Mei et al., 2013a), Advanced Along-Track Scanning Radiometer (AATSR) (Xue et al., 2009;Mei et al., 2013b) and the Jet Propulsion Laboratory (JPL) algorithm for the Multi-angle Imaging Spectroradiometer (MISR) (Diner et al., 2005) are based on the assumption that the surface reflectance can be approximated by a parameter which describes the variation with the wavelength and another one which describes the variation with the geometry (Flowerdew and Haigh, 1995).For geostationary satellites a time series method is employed assuming that the surface reflectance can be selected for each pixel during a certain period of time (Knapp et al., 2002(Knapp et al., , 2005) ) based on the assumption that the surface reflectance does not change significantly during that time period (Mei et al., 2012).In order to avoid cloud shadow effects, the second darkest image is preferred.The operational algorithm used to retrieve the AOD over ocean using Advanced Very High Resolution Radiometer (AVHRR) data (Ignatov et al., 2004) was used for MSG/SEVIRI AOD retrieval (Brindley et al., 2006).In this paper we describe an attempt to retrieve aerosol properties over land from AVHRR data.This is challenging because AVHRR has only two visible bands, which are quite broad, and no mid-infrared channel.Nevertheless, the use of AVHRR data to retrieve aerosol properties is attractive because AVHRR instruments have continuously been in polar orbits, on different satellites, since 1979 (Holben et al., 1992) and thus provide a unique data series for longterm analysis.Xue and Cracknel (1995) developed a retrieval approach using AVHRR data by solving a set of analytical equations.Takemata et al. (2006) derived the surface reflectance at 3.75 µm using the Roger and Vermote (1998) scheme and then established an empirical relationship between the 0.64 µm and 3.75 µm bands using ground-based measurements.However, only 30 points were used for regression, which limited the algorithm to selected land-cover types or certain areas.Hauser et al. (2005) estimated the surface reflectance from a time series including a period of 44 days and then retrieved AOD using a radiative transfer code.Riffler et al. (2010) improved the method from Hauser et al. (2005) by considering a new surface estimating method as well as the aerosol type.Holben et al. (1992) tried to implement a retrieval algorithm previously developed for Landsat data to use with AVHRR data.In this paper we explore an approach in which we assume that the surface reflectance at 0.64 µm can be obtained using an empirical relationship between the reflectances at that wavelength and at 3.75 µm, using the MODIS dark surface approach.After correction for surface effects on the top of atmosphere (TOA) reflectance, the AOD is retrieved using a look-up table (LUT) method adopted from the BAER algorithm (von Hoyningen-Huene et al., 2003, 2011).
A sfc (λ) is the surface spectral albedo, T 1 (λ, µ 0 ) is total transmission of light propagating downward, T 2 (λ, µ) is the total transmission of light propagating upward from the surface to the TOA and s(λ) is the atmospheric hemispherical albedo.
The expressions for T 1 (λ, µ 0 ), T 2 (λ, µ 0 ) and s(λ) can be obtained using the approximate equations from Kokhanovsky et al. (2005).We also used the aerosol phase functions and single scattering albedo from the LACE-98 experiment (von Hoyningen-Huene et al., 2011), which were applied in radiative transfer calculations to build look-up tables (LUT).LUT were used for faster processing by avoiding time-consuming radiative transfer computations during each retrieval.In order to estimate the right item in Eq. (3), Rayleigh path reflectance (R Ray ) and surface reflectance at 0.64 µm (R Surf (0.64 µm)), which is used to calculate surface albedo (A sfc (λ)) are needed.The Rayleigh path reflectance (R Ray ) is determined by the Rayleigh optical depth, τ Ray , (Frohlich and Shaw, 1980) and the Rayleigh phase function, P Ray ( ), is given by Eq. ( 4): where and λ is the wavelength; where is the scattering angle.( 6) To obtain the surface reflectance in the AVHRR visible channel (0.64 µm), we follow the method used in the MODIS dark surface approach.However, because AVHRR does not have a 2.1 µm band, we explore the use of the 3.75 µm channel instead.To do this, the relationship between reflectances at 2.1 µm and 3.75 µm using MODIS data needs to be established (see Fig. 1d).We assume that the aerosol scattering effect can be neglected at both 2.1 µm (Kaufman et al., 1997) and 3.75 µm (Holben et al., 1992).We do not determine the relationship between surface reflectance at 0.64 µm and 3.75 µm directly, because of the uncertainty associated with the 0.64 µm channel surface reflection and required atmospheric correction which depends on AOD which in turn is the parameter we aim to retrieve from AVHRR data.Instead we try to use additional MODIS reflectance products for the evaluation of the statistic relationship, that is, we use the relationship between 2.1 µm and 3.75 µm and the relationship between 2.1 µm and 0.64 µm, all of these obtained from MODIS, separately.
The reflectance at 3.75 µm is given by Eq. ( 7) (Roger and Vermote, 1998;Allen et al., 1990): where R(3.75 µm) is the surface reflectance at 3.75 µm, B(T m 3.75 ) is the Planck function for the temperature T m 3.75 , T m 3.75 is the satellite measurement brightness temperature at 3.75 µm , T e 3.75 is the brightness temperature at 3.75 µm estimated from brightness temperatures and emissivity's in channels 4 and 5 (Roger and Vermote, 1998), L 0 is the solar constant and µ 0 is cosine of solar zenith angle.t 1 is the total transmission of light propagating downward in channel 3, which contains the effect of water vapor and other gases (Roger and Vermote, 1998); t 2 is the total transmission of light propagating upward in channel 3.
Based on the statistical relationship between R Surf (3.75 µm) and R Surf (2.12 µm) and the empirical relationship between R Surf (0.64 µm) and R Surf (2.12 µm) used in the MODIS dark-target algorithm R Surf (0.64 µm) = 0.5 ×R Surf (2.12 µm), we obtain ( The NDVI is determined for AVHRR as where R 0 (0.64 µm) is the reflectance at the TOA at 0.64 µm and R 0 (0.87 µm) is the reflectance at the TOA at 0.87 µm and the NDVI values need to be corrected for AOD effects as proposed by Holzer-Popp et al. (2009).The MODIS surface product (MOD09) was used for the evaluation of Eq. ( 8). Figure 1 demonstrates an example of the statistical parameters (slop, intercept and correlation) between the estimated MODIS 0.66 µm surface reflectance from Eq. ( 8) and the MODIS 0.66 µm surface reflectance product.Figure 1 shows that the estimated surface reflectance correlates well with the MODIS product, with an average uncertainty of ±20 %.
The flowchart for the AVHRR retrieval procedure is shown in Fig. 2. The Earth surface reflectance at 3.75 µm is determined using Eq. ( 7) (Roger and Vermote, 1998) while the Rayleigh path reflectance is calculated using Eq. ( 4).Using the statistical regression Eq. ( 8), the surface reflectance at 0.66 µm can be obtained.Then the aerosol reflectance can be calculated based on Eq. ( 3), which in turn is used to determine the AOD using a simplified LUT method, adopted from the BAER algorithm (von Hoyningen-Huene et al., 2011).In the BAER algorithm, the discrete output from a radiative transfer model (Rozanov et al., 2014) is used to derive parameterisations formulated as polynomials of second degree (von Hoyningen-Huene et al., 2003, 2011).

Study area and data set
Beijing is the capital of China located near the northwest border of the Great North China Plain (See Fig. 3).The region is experiencing serious environmental problems, caused by fast economic development and the resultant release of pollutants from anthropogenic activities such as changes in agricultural and industrial activities, urbanisation and increased traffic, etc.In addition to dust transported from Mongolia which is dominant during the spring and summer, anthropogenic emissions are the main contributors to pollution over Beijing.The pollution levels may become very high due to the location of Beijing at the northern edge of the North China Plain, which is bounded in the north and west by mountain ranges.Winds from the north or west push pollutants out of the city, while those from the south and east result in accumulation of pollutants over the city along the mountain front (http://earthobservatory.nasa.gov/IOTD/view.php?id=38290).Many previous researches show that the AOD over Beijing is often around 0.4-0.5 and sometimes even larger than 2.0 (Sundström et al., 2012).The annual average concentration of PM 2.5 was about 101 µg m −3 in 2001 (He et al., 2001) and about 149 µg m −3 in 2004 (Guinot et al., 2007).
As a result of the relatively large AVHRR swath of approximately 2400 km, the NOAA platforms view the same Earth location twice a day (ascending and descending) and the daytime observation is used for aerosol retrieval.In this work, two channels (0.64 µm and 3.75 µm) of the AVHRR instrument (ascending) on board the polar orbiting NOAA-18 (June and July 2006-2010) and NOAA-19 (June and July 2011) satellites are used.MODIS level 2 aerosol products (MOD04) and MODIS surface reflectance products (MOD09) were used for the comparison of retrieved AOD and surface reflectance derived from AVHRR.For evaluation of the retrieved AODs, sun photometer data from the AERONET (Holben et al., 1998) were used.

Results and validation
As an example, the TOA reflectance measured by AVHRR at 0.64 µm is presented in Fig. 4 together with the surface reflectance derived from that data using Eq. ( 8), the MODIS surface reflectance product at 0.66 µm (MOD09) and the MODIS surface reflectance at 0.66 µm estimated using Eq. ( 8), all for 9 June 2008.Comparison of the images in Fig. 4 shows that the estimated AVHRR reflectance is similar to the MOD09 daily reflectance product.Further analysis shows that 87 % MODIS reflectances in this image are in the range of [0.06-0.1],as compared to 83 % of the AVHRR reflectances.Note that the MOD09 product was resized to the same spatial resolution as AVHRR.
An example of the AOD at 0.64 µm retrieved from AVHRR data over China, using the method presented above is shown in Fig. 5, together with the AVHRR RGB composition map and the cloud map for the same scene, and the MODIS Collection 5 AOD at 0.55 µm.The AVHRR and MODIS AOD show a similar spatial distribution.In this qualitative comparison on the spatial distribution of AOD over the study region, the small difference in wavelength of the two instruments is ignored.The highest AOD values occur in the high population density areas with universities and technology parks.Figure 5 also shows the high AOD to the southwest of Beijing, which may contribute to the pollution in that city due to transport as confirmed by information on wind directions data from http://envf.ust.hk/dataview/gts/current/query_gts_series.py?src_type=ax, which shows that the governing wind direction during the study period was indeed from the southwest.Humidity may be another contributing factor since particle size is sensitive to changes in relative humidity.For instance, the humidity in the southern part was about 60 % while it was about 40 % in the northern part.Much farmland is located in the southwestern part of Beijing, where during summer, the harvest time for crops such as wheat, and biomass burning causes high AODs.
In some areas the AVHRR-derived AOD is low in comparison with MODIS and confirmed by comparison with AERONET.Ignatov (2002) investigated the calibration uncertainty of NOAA_14 AVHRR and estimated an uncertainty in the calibration of ±5-10 %.The calibration is better for NOAA-18 (launched in 2005) and NOAA-19 (launched in 2009), which are used in the paper, but calibration issues still exist (Meirink et al., 2013).An uncertainty in the calibration causes deviation in the TOA reflectance which may result in an increase/decrease of the retrieved surface reflectance, depending on the method of estimation surface reflectance (Hauser et al., 2005), and thus cause an uncertainty in the retrieved AOD.Apart from the calibration problem, there are two other possibilities which may cause underestimation of the AVHRR-retrieved AOD.One could be overestimation of the surface reflectance and the other could be the use of inappropriate aerosol optical properties in the LUTs. Figure 4 shows that the estimated surface reflectance agrees qualitatively quite well with the MOD09 daily surface reflectance product.Hence it is likely that the underestimation is caused by the use of inappropriate aerosol properties in the LUT, especially for high AOD.The absorption is not treated very well in the BAER LUT.Comparison with AERONET data shows that for all match-ups in the Beijing area, the AODs from AVHRR were underestimated.This is similar to earlier findings using the BAER LUT (von Hoyningen-Huene et al., 2011).
The AOD values at 0.64 µm retrieved with our algorithm were evaluated by comparison with collocated sun photometer data provided by the AERONET sites in Beijing, Xianghe and Xinlong from June and July 2006-2011 as well as from another eighteen sites (Bac_Lieu, EPA-NCU, Gosan_SNU, Gwangju_K-JIST, Issyk-Kul, Kanpur, Karachi, MCO-Hanimaadhoo, NCU_Taiwan, Noto, Lulin, Mukdahan, SACOL, Shouxian, Singapore, Taipei_CWB, Ussuriysk, and Yakutsk) during June and July 2008; results are shown in Fig. 6.The overpass time for each site was queried on the AVHRR home page.We follow the validation method presented by Ichoku et al. (2001).Averaged AOD values are used corresponding to an overpass time of ±30 min from the AERONET observation.AOD values derived from AVHRR data were averaged to an area of 50 km × 50 km around the AERONET sites, with the exclusion of pixels where the AVHRR-derived AOD had a standard deviation larger than 0.18 in the 50 km × 50 km window.Such high standard deviations may be caused by apparently enhanced AOD due to undetected clouds.Hence such pixels are excluded to avoid cloud-contaminated pixels.
On the other hand, we reduce the number of LUT in terms of the polynomial by the consideration of single scattering approximation to correct for the different solar and viewing geometries and this approximation is valid for low AOD, but deviates for larger AOD.The deviations start at AOD larger than 1.0 and increase with increasing wavelength.The comparison in Fig. 6 shows 142 match-ups, 71.8 % of which are located within ±(0.1 + 15 %) of the identity line and the correlation coefficient is 0.74.However there is no perfect match with an intercept of around 0.15 and a slope of 0.63.The underestimation is due to the occurrence of absorbing aerosol in the study area which is not included in the BAER LUTs used in the retrieval.Figure 6 also shows that the retrieved AOD is sometimes overestimated, which is due to underestimation of surface reflectance.Cloud contamination may also be a factor here and pixels contaminated with residual clouds may not be completely removed by selection of pixels with a standard deviation of less than 0.18.
The statistical coefficient derived from MODIS data for the relation between the surface reflectances at 0.64 and 2.1 µm is used as prior knowledge in our retrieval method.However, we need to find the empirical relationships for different surface types and in different seasons.MODIS Ångström coefficient product.We can see that the AHVRR and MODIS AOD distributions agree quite well over central and eastern China; however, over western China, AVHRR overestimates the AOD.This is mainly due to the surface properties: the surface over western China is very bright and the dark surface assumption does not apply.Equation (8) may also be invalid for this bright region.As a result, the surface reflectance is underestimated which in turn causes overestimation of the AOD.

Conclusions
An aerosol retrieval algorithm has been presented which uses the single visible band of AVHRR, with support from the infrared channel to determine the surface reflectance.The main problem in aerosol retrieval from AVHRR data is that only one visible wavelength is available.Besides, there are two main limitations for the algorithm presented in this paper.The first one is the effect from the emissivity, which may affect the surface reflectance at 3.75 µm.This effect will not be a great issue for a small study area as used in the study presented here because for such a small area the surface properties are expected be relatively constant (Jin and Liang, 2006).However, for larger areas we need the support of an emissivity data set.The other problem is that a simple LUT was used which has been derived based on a phase function measured during the Lace experiment in 1998 (Von Hoyningen-Huene et al., 2003, 2011) and this phase function may not be representative for the situation over the Beijing area, especially with regards to aerosol absorption.The developed algorithm is the first step towards the use of AVHRR data for the retrieval of AOD over land.

Fig. 1 :
Fig. 1: Statistic parameters between estimated MODIS 0.66µm surface reflectance and MODIS 0.66µm surface reflectance product for June 2008 over East China: (a) Slope; (b) Intercept ;( c) Correlation (R);(d) An example for the scattering plot of surface reflectance between 3.75µm and 2.12µm.

Figure 1 .
Figure 1.Statistic parameters between estimated MODIS 0.66 µm surface reflectance and MODIS 0.66 µm surface reflectance products for June 2008 over eastern China: (a) slope, (b) intercept, (c) correlation (R), and (d) an example of the scattering plot of surface reflectance between 3.75 µm and 2.12 µm.

Figure 2 .
Figure 2. Scheme of the main steps of AVHRR retrieval procedure.

Fig. 2 Figure 3 .
Fig.2 Scheme of the main steps of AVHRR retrieval procedure

LFigure 5 .
Fig. 5 An example of MODIS 0.55µm AOD product (Collection 5) (c) and AVHRR-derived 0.64µm AOD (d) and the corresponding RGB composition map (a) and AVHRR cloud mask product(b) Figure 5.An example of MODIS 0.55 µm AOD product (Collection 5) (c) and AVHRR-derived 0.64 µm AOD (d) and the corresponding RGB composition map (a) and AVHRR cloud mask product (b).

Fig. 7
Fig. 7 Aerosol optical depth distribution of 0.64µm from AVHRR and MODIS/TERRA over China on 9 June 2008.Here MODIS AOD at 0.64µm was converted from AOD at 0.55µm using MODIS Angstrom coefficient product

Figure 7 .
Figure 7. Aerosol optical depth distribution of 0.64 µm from AVHRR and MODIS/TERRA over China on 9 June 2008.Here MODIS AOD at 0.64 µm was converted from AOD at 0.55 µm using a MODIS Ångström coefficient product.