Computationally efficient method for retrieving aerosol optical depth from ATSR-2 and AATSR data

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/7148252 Computationally efficient method for retrieving aerosol optical depth from ATSR-2 and AATSR data ARTICLE in APPLIED OPTICS MAY 2006 Impact Factor: 1.78 DOI: 10.1364/AO.45.002786 Source: PubMed CITATIONS 37 READS 16 3 AUTHORS, INCLUDING: P.R.J. North Swansea University 98 PUBLICATIONS 2,505 CITATIONS Sietse O. Los Swansea University 117 PUBLICATIONS 6,005 CITATIONS SEE PROFILE SEE PROFILE Available from: P.R.J. North Retrieved on: 18 February 2016

Computationally efficient method for retrieving aerosol optical depth from ATSR-2 and AATSR data William M. F. Grey, Peter R. J. North, and Sietse O. Los We present a robust and computationally efficient method for retrieving aerosol optical depth (AOD) from top-of-atmosphere ATSR-2 (Along-Track Scanning Radiometer) and AATSR (Advanced ATSR) reflectance data that is formulated to allow retrieval of the AOD from the 11 year archive of (A)ATSR data on the global scale. The approach uses a physical model of light scattering that requires no a priori information on the land surface. Computational efficiency is achieved by using precalculated lookup tables (LUTs) for the numerical inversion of a radiative-transfer model of the atmosphere. Estimates of AOD retrieved by the LUT approach are tested on AATSR data for a range of global land surfaces and are shown to be highly correlated with sunphotometer measurements of the AOD at 550 nm. (Pearson s correlation coefficient r 2 is 0.71.) 2006 Optical Society of America OCIS codes: 280.1100, 280.1310, 290.1090. 1. Introduction Atmospheric aerosols significantly affect the Earth s radiation budget. Positive and negative radiative forcing may be caused by aerosols, depending on their composition, 1 but the global effect of atmospheric aerosol particles is a net reduction in the amount of solar radiation reaching the Earth s surface 0.5 to 2.5Wm 2 ) that is comparable in magnitude with the positive forcing caused by anthropogenic greenhouse gases 2.0 to 2.5Wm 2 ). 2 Aerosols reduce the amount of surface radiation by reflecting a proportion of the incoming solar radiation back into space. In addition, aerosols play a key role in cloud formation and thus the influence that clouds have on planetary albedo. Despite the importance of the role that aerosols play in the Earth s climate system, the Intergovernmental Panel on Climate Change (IPCC) recognizes that atmospheric aerosols are one of the greatest uncertainties in our understanding of the climate system. 3 This is partly attributed to the lack of accurate and repetitive measurements on global The authors are with the Climate and Land Surface Systems Interaction Centre, School of Environment and Society, Swansea University, Singleton Park, Swansea, SA2 8PP, United Kingdom (e-mail for W. Grey, w.m.f.grey@swan.ac.uk). Received 18 July 2005; revised 20 September 2005; accepted 16 November 2005; posted 16 November 2005 (Doc. ID 63500). 0003-6935/06/122786-10$15.00/0 2006 Optical Society of America scales. 4 Atmospheric aerosols need to be continuously monitored owing to their dynamic nature. Typically, aerosols have short atmospheric residence times of the order of days to weeks and are derived from relatively local sources; so their distribution and composition are highly variable. Satellite remote sensing offers a means for routinely measuring aerosols on global scales. Several products have been developed that provide routine measurements of aerosol properties including the Total Ozone Mapping Spectrometer (TOMS), 5,6 the Multiangle Imaging SpectroRadiometer (MISR), 7 the Moderate Resolution Imaging Spectrometer (MO- DIS), 8 and the Advanced Very High Resolution Radiometer (AVHRR). 9 13 Although there is nearly a 3 decade record of TOMS aerosol measurements on the global scale, these observations are often contaminated by cloud owing to the large footprint of the sensor. 6 The AVHRR aerosol product also provides a long time series of measurements. Although these retrievals are currently limited to the ocean, aerosol properties could be retrieved over land. 14 Intercomparisons of satellite retrievals of aerosol optical depth (AOD) from the TOMS, AVHRR, and other instruments have shown that there are significant differences in the retrieved AOD over many ocean sites. 15,16 MODIS and MISR offer improved estimates of aerosol properties but have relatively short archives. Thus a long time record of accurate estimates of aerosol properties on a global scale are needed. Here we use top-of-atmosphere Along-Track Scanning Radiometer (ATSR-2) and Advanced ATSR 2786 APPLIED OPTICS Vol. 45, No. 12 20 April 2006

(AATSR) reflectance data for retrieving atmospheric aerosol properties. This is a unique contribution because (A)ATSR provides a long-term record of accurate estimates of aerosol properties at regional and global scales over the duration of the satellite missions from 1995 to the present day. The ATSR-2 and AATSR instruments, launched onboard the European Remote Sensing (ERS-2) and Envisat satellites in 1995 and 2002, respectively, form part of the European Space Agency s Earth observation program for long-term environmental monitoring on global scales. 17 For all practical intents, both instruments are identical and acquire two simultaneous observations of the same area of the Earth s surface through different atmospheric path lengths at view zenith angles of 55 (the forward view) and 0 (the nadir view). Dual view-angle observations allow the properties of the atmosphere to be inferred without the need for a priori information concerning the land surface. The (A)ATSR swaths are approximately 500 km wide, and the nominal size of each pixel at nadir is 1 km 1 km. There are 7 spectral bands, but only the 4 bands in the optical region (555, 670, 870, and 1610 nm) are used for aerosol retrieval. These spectral bands are narrow 20 nm and avoid the atmospheric water vapor absorption regions. Multi-view-angle observations from instruments such as MISR and ATSR-2 provide improved aerosol estimates compared with single-look observations. 18 However, using multi-angle observations for retrieving aerosol properties is difficult because surface reflectance at optical wavelengths depends on the Sun and sensor geometry. Variations in reflectance between simultaneous multi-angular measurements of the ground are caused by surface scattering in addition to the differences in the atmospheric path length. To separate the atmospheric properties and surface reflectance from multi-angle measurements, the angular variations due to atmospheric and surface scattering need to be taken into account. In Ref. 19 a simple physical model of light scattering is developed that allows us to obtain atmospheric aerosol properties. The model also allows us to remove the effects of atmospheric scattering and absorption from top-of-atmosphere reflectance so that surface reflectance can be obtained. Previous research with (A)ATSR for retrievals of aerosol properties has primarily been concerned with the development and testing of algorithms. 19 21 Estimates of the (A)ATSR-derived AOD can be retrieved for different aerosol types and land covers, including bright desert surfaces. 22 Satellite-based retrievals of aerosol properties have also been driven by the need to remove the effects of atmospheric scattering and absorption from top-of-atmosphere remotely sensed observations in order to obtain surface reflectance. This is necessary for quantitative estimates of land surface biophysical properties 23,24 and time-series analysis. 25 We present a robust and computationally efficient method for retrieving estimates of the AOD from (A)ATSR that can be applied operationally at regional and global scales. Computational efficiency is achieved by using precalculated lookup tables (LUTs) for the numerical inversion of a radiative-transfer model of the atmosphere instead of the full inversion approach that is more computationally intensive. We minimize the number of input model parameters and therefore the dimensions of the LUTs through a sensitivity analysis of retrieved values of the AOD to perturbations in a range of input parameters. The influence of the LUT grid density on the accuracy of the AOD estimates is also examined. Estimates of the AOD retrieved with the LUT approach are tested over a range of land surface types against estimates of the AOD retrieved by full inversions and sunphotometer measurements. To evaluate the speed of the LUT method and its application over very large areas, estimates of the AOD were retrieved over Northern Africa and Europe in October 2004. 2. Model of Surface Scattering Satellite observations at optical wavelengths consist of solar radiation scattered by both the atmosphere and the surface. The atmospheric and the surface contributions to the reflectance viewed by a spaceborne sensor at the top of the atmosphere R toa can be expressed as 26 R toa, s, v, T G, s, v R a, s, v, T, s T, v R surf, s, v, 1 R surf, s, v, S, (1) where is the wavelength, v is the view zenith angle, s is the solar zenith angle, is the relative azimuth angle between the solar and the viewing positions, T G is the total gaseous transmittance through the atmosphere, R a is the atmospheric reflectance due to Rayleigh and aerosol scattering, R surf is the surface reflectance, and S is the spherical albedo of the atmosphere. T v is the total transmittance between the surface and the sensor: T v exp cos v, (2) and T s is the total transmittance of the atmosphere on the path between the Sun and the surface: T s exp cos s, (3) where is the combined aerosol and Rayleigh optical depth of the atmosphere. R toa, s, v, is a function view and illumination angle as well as wavelength and is defined as L F 0, where L is the radiance measured by the satellite and F 0 is the irradiance at the top of the atmosphere. The 1 R surf, s, v, S term describes the multiple interaction between the surface and the atmosphere. We need to solve the inverse problem and separate the atmospheric and surface scattering contributions 20 April 2006 Vol. 45, No. 12 APPLIED OPTICS 2787

to the observed signal. A physical model of light scattering developed in Ref. 19 allows us to retrieve estimates of the atmospheric AOD at 550 nm, aerosol type (e.g., desert-dust, smoke, and maritime), and the surface bidirectional reflectance given a set of top-ofatmosphere reflectances for the four optical (A)ATSR channels in the nadir and forward view directions without the need for a priori information on the land surface. The angular variation of reflectance depends on the three-dimensional structure of the surface. Surface scattering is dominated by wavelength-independent geometric effects because the scattering elements are much larger than light at optical wavelengths. Since the geometric structure of the surface does not vary with wavelength, there will be some correlation between the bidirectional reflectance distribution functions at different wavelengths even though the optical properties of scattering elements may be wavelength dependent. Scattering by atmospheric aerosols increases the diffuse contribution of light at the surface. Owing to the interreflection of light between the surface scattering elements, the anisotropy is reduced when the diffuse irradiance is high because the contrast between shadowed and sunlit surfaces decreases. The atmospheric scattering elements including aerosols and gas molecules are approximately the same size and smaller than light at optical wavelengths, and so the effect of atmospheric scattering on the anisotropy is wavelength dependent. The surface bidirectional reflectance R mod may be decomposed into a component that is independent of view direction w and a component that is independent of wavelength P: R mod, 1 D P w w 1 g D g 1 D, (4) where g 1 w, is the view direction, is the fraction of multiple scattering, and D is the fraction of diffuse irradiance. The first term in the model refers to single scattering, and the second term refers to multiple scattering. In Ref. 19 the range of retrieved values for was shown to vary from 0.19 to 0.6. In the inversion the effect of increasing is to decrease the anisotropy of surface scattering. However, a similar effect can be achieved by decreasing the ratio of retrieved P(f) top(n), and so the retrieval of the AOD is not significantly sensitive to the retrieved value. Here P(f) and P(n) are the values for P in the forward and the nadir view directions, respectively. Experiments performed in Ref. 19 with a large data set of natural surface reflectances showed that a fixed value of 0.3 for results in increased efficiency without significant loss of accuracy. The angular reflectance of a wide variety of natural land surfaces has been shown to fit this simple model. 19 In contrast, reflectance that is a mixture of atmospheric and surface scattering does not fit this model well. As a result the model can be used to estimate the degree of atmospheric contamination for a particular set of reflectance measurements and to find the atmospheric parameters that allow retrieval of a realistic ground reflectance. Our aim is to retrieve the parameters characterizing the atmospheric aerosol and ground reflectance from cloud-free top-of-atmosphere reflectance data. This is achieved through inversion of the Second Simulation of the Satellite Signal in the Solar Spectrum (6S) radiative-transfer model. 26 The derived parameters include a set of eight surface reflectance values for the four visible and near-ir AATSR bands in both the nadir and the forward views, an AOD at 550 nm, and an estimate of the tropospheric aerosol model that falls into one of the five standard tropospheric aerosol models presented in 6S. These aerosol models include continental (predominantly composed of dustlike particles), urban (mainly sulfates), maritime (sea salts), biomass (carbonaceous smoke particles), and desert dust. The aerosol microphysical properties (the refractive index and the size distribution function) have been parameterized in each aerosol model. We derive an AOD at 550 nm because the 6S radiative-transfer model paramaterizes the AOD by its value at 550 nm. In 6S the AODs at other wavelengths are calculated according to the aerosol model determined during the inversion. The 6S takes into account the asymmetry of the aerosol particle scattering. We solve the inverse problem through iteration of a two-stage numerical process. 27 In the first stage we retrieve a set of eight ground reflectance values and estimates of diffuse irradiance at the four wavelengths, given an estimate of the atmospheric aerosol model and the AOD at 550 nm by the inversion of 6S. We converge on the optimal values of P and w so that the estimates of surface reflectance across the four channels and two directions most closely resemble the surface reflectance calculated for a given atmospheric aerosol model and AOD at 550 nm. The second stage uses the Brent line minimization 28 to search through different atmospheric profiles to find the AOD and aerosol model that results in the optimal set of surface reflectance data. For each iteration, each estimate of AOD and aerosol model results in a different set of surface reflectance values. The optimum value of AOD is the best fit of surface reflectances to the model [Eq. (3)] and is attained by minimizing the error function E mod : 2 E mod 1 4 1 R surf, R mod, 2, (5) where R surf is the surface reflectance calculated for a given estimate of AOD at 550 nm and the aerosol model when 6S is used and R mod is the surface reflectance estimated by using Eq. (3) based on the values of P and w. The reflectance contaminated with atmospheric scattering cannot fit the equation, and a high E mod residual error implies that the atmosphere has not been accurately corrected for. The uncertainty in the retrieved values of AOD depends on the ambigu- 2788 APPLIED OPTICS Vol. 45, No. 12 20 April 2006

ity of the optimal solution of Brent minimization. Brent minimization uses parabolic interpolation to converge on the minimum value, and the second derivative (i.e., curvature) of the parabola is related to the measurement error, 28 where a high degree of curvature results in a low uncertainty. The most appropriate aerosol model is also selected on the basis of the best fit by minimizing E mod. The accuracy of the AOD estimates depends on how well the aerosol model characterizes the atmospheric profile, but it does assume that the aerosol model that best characterizes the atmospheric profile minimizes E mod. The flexibility in the selection of the aerosol model allows us to take account of the spatial and the temporal variability of aerosol microphysical characteristics. 3. Data The model of surface scattering was applied to both simulated and real AATSR data. Simulated data were used for the sensitivity analysis so that the model could be implemented over the full range of the (A)ATSR angular domains for a variety of land surfaces. A simulated data set that reproduced the expected (A)ATSR reflectance in the four optical channels in both directions as described in Ref. 19 was used. Top-of-atmosphere reflectances were generated for a range of land covers by using the threedimensional Monte Carlo ray-tracing code of Ref. 29 coupled with the 6S radiative-transfer model of the atmosphere for AOD values of 0.1, 0.4, and 0.7 and several aerosol types. The US62 standard atmospheric profiles were used with an ozone column of 0.35 cm atm, a water vapor column of 2.5 g cm 2, and a surface elevation of 0.5 km. To test the LUT in operation, model inversions were performed on 174 level 1b gridded brightness temperature and reflectance (GBTR) AATSR images for 12 sites across the world representing a range of land surfaces and aerosol sources. Although inversions have been performed only on AATSR data, the model can also be applied directly to ATSR-2. Preprocessing of the AATSR involved averaging pixels within a 15 km 15 km area to reduce the effect of coregistration errors between the nadir and the forward directions and masking cloudy pixels by applying a set of tests to the near-ir and thermal channels. 30 The AATSR test sites were selected to coincide with the sites of the Aerosol Robotic Network (AERO- NET) sunphotometer instruments. 31 AERONET is a global network of ground-based sunphotometers that measures sky radiance from which AOD and other atmospheric properties can be derived. The sunphotometers were used for testing the accuracy of the AATSR-derived estimates of the AOD. 4. Lookup Tables Performing inversions by using repeated forward model runs of atmospheric radiative-transfer models is computationally expensive. Several approaches have been developed that increase the speed of numerical inversions including the use of LUTs, 32 neural networks, 33 and semiempirical parameterizations. 34 When LUTs and neural networks are used, the most computationally expensive aspect is completed before inversion. Here we use LUTs created from forward runs of the 6S atmospheric radiative-transfer model that are composed of coefficients describing the transmission, incident radiance, and surface reflectance. These coefficients are sampled at regular intervals for the four visible and near-ir channels of (A)ATSR across a range of sun-sensor geometries, values of the AOD at 550 nm, and other key atmospheric properties. The LUTs are generated for the five tropospheric aerosol models. To avoid quantization, the values are estimated in the LUTs by using multidimensional piecewise linear interpolation between the grid points. There will inevitably be a small decrease in the accuracy of the retrieved measurements when compared with full inversions, but this is offset by an increase in speed of several orders of magnitude. A. Minimizing Lookup Table Dimensions For accurate estimates of AOD and surface reflectance, the LUTs need to include a large range of atmospheric parameters. These input parameters are sometimes unknown, and we often use a priori assumptions to constrain the inverse problem. Parameters that have little or no effect on the output should not be included unnecessarily in the LUTs. This is because the number of input parameters is equal to the number of dimensions in the LUTs, and there is a geometric increase in the LUT size with each additional parameter. Hence generating large LUTs with numerous parameters requires a correspondingly large computational overhead. We minimize the number of dimensions in the LUT by including only those parameters to which the output is sensitive. A sensitivity analysis was performed in order to investigate the uncertainty in the retrieved values of AOD to perturbations in a range of atmospheric parameters, including column integrated concentrations of ozone and water vapor and surface elevation. Concentrations of many of the atmospheric gases are relatively constant and can be parameterized, but water vapor and ozone concentrations are highly variable. Surface elevation is also important because it influences the length of the atmospheric column and consequently the amount of scattering and absorption in the atmosphere. Sensitivity analysis involves perturbing the input parameters of interest within the range of likely uncertainty and examining the effect that this has on the output. The sensitivity study was performed on the simulated (A)ATSR data set. Full model inversions were preformed on the simulated top-of-atmosphere data, assuming an accurate atmospheric profile (aerosol model), but with perturbed values of atmospheric ozone and water vapor concentrations, and surface elevation as shown in Table 1. The sensitivity analysis was performed with the variance-based approach described in Ref. 35. The sensitivity of the output to an 20 April 2006 Vol. 45, No. 12 APPLIED OPTICS 2789

Table 1. Perturbed Values of Atmospheric Ozone and Water Vapor Concentrations and Surface Elevation Used in the Sensitivity Study Parameter Forward Modeled Minimum Perturbation Maximum Perturbation Ozone (cm atm) 0.35 0.10 0.50 Water vapor (g cm 2 ) 2.5 0.0 6.0 Elevation (km) 0.5 0.0 2.0 Note: The values used in forward runs of the model for creating the top-of-atmosphere simulated data are also given. individual input parameter X i (i.e., the main effect) is given as the conditional variance E Y Xi 2. The expectation E of the output estimate Y is conditional on a fixed value of X i. For higher-order interactions the expectation of Y is conditional on fixed values of multiple input parameters. The results of the sensitivity analysis are summarized in Table 2. The estimates of AOD are sensitive to the perturbation in the surface elevation, as highlighted by a high conditional standard deviation. An incorrect surface elevation causes an inaccurate estimate of Rayleigh scattering and gaseous absorption, and as a result estimates of Mie scattering caused by aerosols will also be inaccurate. For example, if the atmospheric column is overlengthened (i.e., the surface elevation is assumed to be too low), the AOD is underestimated. Perturbations in atmospheric ozone concentrations also cause uncertainty in the AOD estimates. When ozone concentrations are overestimated the AOD is also overestimated because the model assumes an increased Mie scattering to compensate for the augmented effects of the gaseous absorption caused by overestimating ozone concentrations. The effect of perturbing the atmospheric water vapor content has a negligible effect on AOD. This is expected because the narrow (A)ATSR reflectance channels are at wavelengths at which water vapor transmittance is nearly 100%. Higher-order interactions between the three parameters are also negligible. Based on this sensitivity study, atmospheric ozone concentrations and surface elevation are included in the LUTs. To test how accurately the mathematical model describes the physical reality, the AOD was calculated for an idealized case in which the atmosphere can be perfectly characterized. In this case the same atmospheric parameters that we used to create the topof-atmosphere reflectance data were used for the inversion. As presented in Table 2, the difference in the model-retrieved AOD and actual AOD is less than 0.02 in the majority of cases. In cases in which the measurement error is high, the second derivative of the Brent minimization is small. This suggests that the Table 2. Conditional of the Retrieved Estimates of AOD by Using the Full Inversions for Perturbed Values of Atmospheric Ozone and Water Vapor Concentrations and Surface Elevation Land Surface (and Aerosol Model) Simulated AOD Retrieved AOD for Ideal Case Curvature of Brent Parabola (10 4 ) Water Vapor Ozone Elevation Total Relative Azimuth Angle Dense forest (smoke) 0.7 0.682 0.31 0.002 0.011 0.065 0.068 0 30 0.4 0.395 4.56 0.000 0.001 0.011 0.011 180 30 0.1 0.076 6.17 0.000 0.003 0.014 0.015 90 60 Sparse forest (smoke) 0.7 0.159 0.01 0.004 0.070 0.055 0.104 0 30 0.4 0.393 2.31 0.000 0.002 0.008 0.008 180 30 0.1 0.068 0.90 0.000 0.006 0.011 0.013 90 60 Homogenous canopy bright soil green vegetation (continental) Solar Zenith Angle 0.7 0.703 0.33 0.000 0.014 0.075 0.076 0 30 0.4 0.377 2.83 0.000 0.005 0.005 0.007 180 30 0.1 0.084 2.28 0.000 0.006 0.018 0.019 90 60 Homogenous canopy bright soil 0.7 0.678 0.08 0.007 0.034 0.062 0.071 0 30 sensecent vegetation 0.4 0.358 0.83 0.001 0.015 0.005 0.016 180 30 (continental) 0.1 0.068 0.63 0.001 0.022 0.021 0.030 90 60 Homogenous canopy dark soil green vegetation (smoke) Homogenous canopy dark soil sensecent vegetation (smoke) 0.7 0.721 0.37 0.001 0.011 0.061 0.062 0 30 0.4 0.392 3.68 0.000 0.003 0.004 0.005 180 30 0.1 0.089 2.49 0.000 0.005 0.017 0.018 90 60 0.7 0.750 0.08 0.003 0.040 0.068 0.079 0 30 0.4 0.386 1.09 0.001 0.013 0.004 0.013 180 30 0.1 0.087 0.80 0.001 0.018 0.019 0.026 90 60 Bare soil (desert dust) 0.7 0.739 0.16 0.001 0.009 0.095 0.096 0 30 0.4 0.404 4.93 0.000 0.000 0.014 0.014 180 30 0.1 0.113 2.02 0.000 0.001 0.019 0.020 90 60 Bare soil (continental) 0.7 0.694 0.15 0.001 0.010 0.081 0.082 0 30 0.4 0.403 8.80 0.000 0.000 0.018 0.018 180 30 0.1 0.100 3.89 0.000 0.001 0.024 0.024 90 60 Note: Total for all parameters is also presented. The inversions are performed on the simulated data set over a range of land surfaces, aerosol models, and sun-sensor geometries. The continental aerosol model is predominantly composed of desert dust. The retrieved aerosol for AOD is calculated, assuming an ideal characterization of the atmospheric profile. 2790 APPLIED OPTICS Vol. 45, No. 12 20 April 2006

Table 3. Summary of Statistics of Intercomparison between the AATSR Derived Estimates of AOD at 550 nm Calculated by Using the Full Model Inversions and the LUT Inversions for All Sites Combined at Different Sampling Densities AERONET Full Inversion VZA Interval RAZ Interval SZA Interval AOD at 550 nm Interval Number of Samples in LUT r 2 RMSE Mean Error r 2 RMSE 5.0 20.0 5.0 0.05 212000 0.71 0.18 0.008 1.00 0.02 0.003 5.0 20.0 5.0 0.10 109200 0.74 0.17 0.037 0.99 0.05 0.032 5.0 20.0 5.0 0.20 57200 0.74 0.17 0.041 0.99 0.05 0.036 5.0 60.0 5.0 0.05 85280 0.73 0.17 0.044 0.97 0.08 0.040 5.0 20.0 10.0 0.05 114800 0.73 0.17 0.039 0.99 0.05 0.034 10.0 20.0 5.0 0.05 68880 0.74 0.17 0.055 0.99 0.07 0.051 Note: The ozone and surface elevation intervals are 0.4 cm atm and 2 km, respectively and are the same for all table sizes, whereas the view zenith angle (VZA), relative azimuth angle (RAZ), and solar zenith angle (SZA) intervals are changed. Mean Error error is associated with the numerical method and not because the model poorly represents the physics. B. Lookup Table Size In this experiment the influence of the LUT grid density on the accuracy of the AOD estimates is examined. During operation the values are estimated in the LUT by multidimensional piecewise linear interpolation. Densely sampled LUTs reduce the error in the retrieved AOD estimates compared with sparsely sampled LUTs but at a greater computational overhead of generating more samples. We aim to find the optimal trade-off between accuracy and LUT size. The goal is to retrieve LUT-derived estimates of AOD that are within the root-meansquare error of 0.02 for estimates of AOD derived from the full inversions. 27 The influence of the LUT grid density on the accuracy of the AOD estimates is examined. Six-dimensional LUTs of coefficients at the four optical (A)ATSR channels were created at a range of solar zenith angles (from 20 to 80 ), view zenith angles (from 0 to 60 ), relative azimuth angles (from 0 to 180 ) and AOD at 550 nm (from 0 to 2), atmospheric ozone concentration (from 0.1 to 0.5), and surface elevation (from 0 to 2 km) were created with 6S. To take account of the atmospheric ozone absorption, TOMS ozone data were used. Ancillary height information from the GTOPO30 (global 30 arcsecond topographic map) was also input into the model. The LUT-derived estimates of the AOD are compared with sunphotometer observations and with the estimates of AOD retrieved by using the full inversions across all sites combined (see Table 3). The estimates of AOD retrieved by using the LUT and full inversions are well correlated for all LUT sizes (Pearson s correlation coefficient r 2 values of greater than 0.95). In general, the fewer the number of samples in the LUT, the larger the underestimate (mean error) in the retrieved values of AOD, although this depends on which parameters are subsampled. The estimates of AOD derived from the largest LUT are within an RMSE of 0.02 for estimates of AOD derived from the full inversions (see Fig. 1). The estimates of AOD derived by the largest LUT are compared with sunphotometer observations and with the estimates of AOD retrieved with the full inversions at individual sites as presented in Table 4. The range of r 2 between the sunphotometer measurements and the LUT-derived AOD varies from 0.14 at Lake Argyle to 0.96 at Solar Village. The algorithm tends to perform best over homogeneous vegetated areas with relatively low reflectances in the visible channels, such as Lille, Cart Site, Jabiru, and Konza. The algorithm also performs well over heterogeneous semi-arid land covers such as Ouagadougou in the Sahel. At Kanpur and Solar Village the estimates of AOD tend to be overestimated, hence the high mean errors. Figure 2 shows a comparison of the LUT-derived estimates of AOD and the sunphotometer AOD across all sites combined, where Pearson s r 2 is 0.71. The error of the residuals tends to increase with increasing AOD. The RMSE of all the data is 0.17; but when only AOD values less than 0.5 (as derived from Fig. 1. Comparison between the AATSR-derived estimates of AOD at 550 nm calculated with full model inversions and inversions with the largest LUT (212000 grid samples) for all sites combined. The 1:1 line is shown. 20 April 2006 Vol. 45, No. 12 APPLIED OPTICS 2791

Table 4. Summary of Statistics of Intercomparisons between AATSR Estimates of AOD Derived using the Largest LUT, Sunphotometer Observations, and Estimates of AOD Retrieved from the Full Inversions at Individual Sites AERONET Full Inversion Site Land Cover Time period Number of samples Aerosol model Mean R surf for forward view at 660 nm Mean AOD rms at 550 nm r 2a Error Mean rms Error r 2a Error Mean Error Alta Floresta, Brazil ( 9.9 N, 56.0 E) Banizoumbou, Niger (13.5 N, 2.7 E) Cart Site, United States (36.6 N, 97.4 E) Jabiru, Australia ( 12.7 N, 132.9 E) Kanpur, India (26.5 N, 80.4 E) Konza, United States (39.1 N, 96.6 E) Lake Argyle, Australia ( 16.1 N, 128.7 E) Lille, France (50.6 N, 3.1 E) Oostende, Belgium (51.2 N, 2.9 E) Oungadougou, Brkina Faso (12.2 N, 1.4 E) Phimai, Thailand (15.2 N, 102.6 E) Solar Village, Saudi Arabia (24.9 N, 46.4 E) Primary forest, agriculture 28 11 02 26 09 03 Arid 18 10 02 17 09 03 Prairie, agriculture Tropical forest 09 05 03 06 03 04 02 06 03 01 10 03 Urban 23 03 03 07 03 04 Prairie 25 09 02 27 12 03 Semiarid rangeland Urban, agriculture Urban, agriculture Semiarid. tropical Urban, tropical 15 12 02 20 01 04 14 08 02 07 12 03 14 08 02 22 09 03 30 10 02 28 01 04 11 04 03 31 12 03 Arid 04 10 02 09 03 04 All sites 14 08 02 09 03 04 4 Biomass 0.08 0.37 0.61 0.19 0.079 0.99 0.01 0.002 13 Biomass and maritime 0.27 0.65 0.64 0.24 0.087 0.99 0.03 0.016 11 Biomass 0.08 0.15 0.80 0.04 0.005 0.99 0.01 0.005 7 Maritime 0.09 0.11 0.90 0.05 0.013 0.99 0.01 0.001 15 Biomass 0.14 0.43 0.81 0.31 0.191 0.99 0.01 0.002 18 Biomass 0.08 0.11 0.83 0.04 0.027 0.99 0.01 0.004 7 Maritime 0.14 0.08 0.14 0.07 0.016 0.92 0.02 0.003 7 Biomass 0.08 0.14 0.91 0.04 0.008 0.99 0.00 0.002 7 Biomass 0.07 0.21 0.57 0.08 0.021 0.99 0.00 0.003 28 Desert, biomasss and maritime 0.19 0.43 0.77 0.18 0.057 0.99 0.02 0.002 5 Biomass 0.11 0.34 0.64 0.14 0.038 0.99 0.01 0.005 25 Desert and maritime 0.37 0.39 0.96 0.21 0.143 0.99 0.02 0.000 147 0.31 0.71 0.18 0.008 0.99 0.02 0.003 a Italicized r 2 values are significant to the 95% confidence level. 2792 APPLIED OPTICS Vol. 45, No. 12 20 April 2006

accurately characterized; thereby a better estimate of AOD is achieved in addition to aerosol type. Alternatively the aerosol model could be a priori constrained for a likely aerosol source for a given location and time of year. Fig. 2. Comparison between the LUT-derived estimates of the AOD at 550 nm with sunphotometer measurements for all sites combined. The error bars correspond to the reported uncertainty in AERONET measurements of AOD, which is given as 0.02. The 1:1 line is shown. the sunphotometers) are considered, the RMSE is reduced to 0.09. In addition to the errors caused by interpolation of the LUTs, the differences between the sunphotometer and AATSR-derived estimates of AOD may also be caused by small time differences between the acquisition of sunphotometer measurements and the satellite overpass, undetected subpixel cloud contamination, the selection of an aerosol model that does not properly characterize the atmospheric scattering, and heterogeneity of the land surface within the 15 km 15 km area of AATSR observations. The selected aerosol models are consistent with the likely aerosol source and land cover for some of the sites. For example, at Alta Floresta, a region of the primary forest site in the Amazon, the biomass model is selected, and at Jabiru, situated at a coastal location, the maritime model is chosen on the basis of the best fit to the model. Despite these cases this method does not reliably predict the most likely aerosol model for a given land cover. At Ouagadougou in the Sahel the biomass, desert-dust, and maritime models are selected. Although biomass and desert-dust aerosols are likely due to burning vegetation during spring and aeolian-transported dust from the Sahara, maritime aerosols in this region are highly unlikely. At Solar Village in the Saharan desert the desert-dust model is selected in addition to the maritime model that we do not expect. For other sites such as Banizoumbou and Lake Argyle inappropriate models are selected in all situations. Moreover the retrievals of AOD would be improved if the aerosol model accurately characterized the atmospheric profile. By increasing the number of aerosol models and including mixtures of different types of aerosol, the atmosphere is more likely to be 5. Aerosol Optical Depth over Northern Africa and Europe To evaluate the speed of the LUT approach and its application over very large areas, estimates of AOD are retrieved over Northern Africa and Europe for the first 6 days of October 2004. A map of the AOD at 550 nm over this region is presented in Fig. 3, and the inversions are performed by using the largest LUTs (212,000 grid samples). The composite is composed of eight 500 km wide AATSR strip lines that are approximately 8000 km in length. Although the atmosphere is relatively clear over Northern Europe, the AOD is high (as high as 0.7 at 550 nm) over the Sahara. The Sahara is a robust test for the algorithm because it is difficult to retrieve aerosol properties over bright surfaces such as deserts. It takes approximately 1.5 h to process data from 1 orbit, depending on the extent of cloud cover, on a personal computer with an Intel Xeon 2.8 GHz microprocessor and 1 GB of DDR266 (double data rate) RAM. Retrieving surface reflectance in addition to AOD requires a threefold increase is processing time because bidirectional reflectance is retrieved at a finer resolution. For each orbit, only the descending node is processed because the ascending node data are acquired at night. Envisat orbits the Earth approximately 14 times a day, and each orbital AATSR strip line is nearly 1 GB in size. The LUTs facilitate the retrieval aerosol properties at global scales on a routine basis when relatively modest computational resources are used. 6. Conclusions We have developed a robust and efficient method that has the potential for the retrieval of AOD from topof-atmosphere (A)ATSR reflectance data. This approach uses precalculated LUTs for the numerical inversion of a radiative-transfer model of the atmosphere and provides a 60-fold increase in speed when compared with full inversions, with only a small trade-off in accuracy. This makes possible the retrieval of AOD from the 11 years of archived (A)ATSR data at regional and global scales without the need for a priori information of the land surface. Through a sensitivity study it was shown that AOD is very sensitive to perturbations in surface elevation. Perturbations in atmospheric ozone concentrations also cause some uncertainty in the retrieved AOD, whereas the effect of perturbing the atmospheric water vapor content has a negligible effect and was not included in the LUT. The retrieval of AOD estimates with LUT inversions was tested over a range of land surface types and shown to be highly correlated with the AOD retrieved by using full inversions and sunphotometer measure- 20 April 2006 Vol. 45, No. 12 APPLIED OPTICS 2793

Fig. 3. Map (color online) of AATSR-retrieved AOD at 550 nm of Northern Africa and Europe during the first week in October 2004. The composite is made up of eight 500 km wide AATSR strip lines that are approximately 8000 km in length. ments. (Pearson s r 2 is 0.71.) Misidentification of the aerosol type can cause errors in the estimates of AOD, but, by using a larger range of aerosol models that better characterize the atmosphere, we can improve our estimates of AOD. This research was funded by the United Kingdom Natural Environment Research Council through the Climate and Land Surface Systems Interactions Centre (CLASSIC). We gratefully acknowledge the European Space Agency for providing the AATSR data through the Announcement of Opportunity for Envisat. We thank the AERONET principal investigators and their staff for establishing and maintaining the AERONET sites used in this investigation. The TOMS ozone data were acquired from the Goddard Space Flight Centre and the GTOPO30 data from the United States Geological Survey. References 1. M. I. Mishchenko, B. Cairns, J. Chowdhary, I. V. Geogdzhayev, L. Liu, and L. D. Travis, Remote sensing of terrestrial tropospheric aerosols from aircraft and satellites, J. Phys. Conf. Ser. 6, 73 89 (2005). 2. J. T. Kiehl and B. P. Briegleb, The relative roles of sulfate aerosols and greenhouse gases in climate forcing, Science 260, 311 314 (1993). 3. J. T. Houghton, Y. Ding, D. J. Griggs, M. Noguer, P. J. van der Linden, and D. Xiaosu, eds., Climate Change 2001: The Scientific Basis (Cambridge University, 2001). 4. Y. J. Kaufman, D. Tanré, and O. Boucher, A satellite view of aerosols in the climate system, Nature (London) 419, 215 223 (2002). 5. N. C. Hsu, J. R. Herman, O. Torres, B. N. Holben, D. Tanré, T. F. Eck, A. Smirnov, B. Chatenet, and F. Lavenu, Comparisons of the TOMS aerosol optical thickness: results and applications, J. Geophys. Res. 104, 6269 6279 (1999). 6. O. Torres, J. R. Herman, P. K. Bhartia, A. Sinyuk, P. Ginoux, 2794 APPLIED OPTICS Vol. 45, No. 12 20 April 2006

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