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GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L06807, doi:10.1029/2008GL033231, 2008
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On reflectance ratios and aerosol optical depth retrieval in the presence of cumulus clouds Evgueni I. Kassianov1 and Mikhail Ovtchinnikov1 Received 11 January 2008; accepted 25 February 2008; published 28 March 2008.
[1] The traditional conversion of satellite-observed reflectances to the aerosol optical depth (AOD) is highly conjectural in the vicinity of clouds due to the 3D cloudinduces enhancement of the apparent reflectance. This study uses 3D Monte Carlo radiative transfer calculations and simulated cloud and aerosol fields to illustrate that for clear pixels the reflectance ratios for two pairs of wavelengths (660, 470 nm and 870, 470 nm) are less sensitive to the 3D cloud effects than the reflectances themselves. We develop a new algorithm for converting these two ratios to three spectral values of AOD and show that it is accurate to within 10% for the majority of clear pixels in our model-inverse problem. This preliminary study suggests that the proposed approach can be used to significantly improve the accuracy of the AOD retrieved from spectral satellite observations under partly cloudy conditions. Citation: Kassianov, E. I., and M. Ovtchinnikov (2008), On reflectance ratios and aerosol optical depth retrieval in the presence of cumulus clouds, Geophys. Res. Lett., 35, L06807, doi:10.1029/2008GL033231.
1. Introduction [2] Estimating the aerosol optical depth, t a, in the vicinity of clouds is a long-standing problem. Large spatial and temporal variability of clouds, their complex threedimensional (3D) geometry and related uncertainties in cloud screening present major challenges to satellite aerosol retrievals [e.g., Ackerman et al., 1998; Zhang et al., 2005]. Using Monte Carlo radiative transfer (RT) simulations and a cumulus cloud field derived from the MODerate-Resolution Imaging Spectroradiometer (MODIS) data, Wen et al. [2006] showed that even for clear areas 3 km away from clouds, the 3D effects can increase substantially the clear sky reflectance and, therefore, lead to significant overestimation of t a. The long-term MODIS aerosol statistics obtained in clear patches of cloud fields may be largely in error (up to 140%) as a result of the 3D cloud-induced enhancement of clear sky reflectance [Wen et al., 2007]. [3] The purpose of this paper is threefold. First, we assess the importance of the 3D cloud effects on the reflectance ratios for pixels located far away from clouds and their shadows (clear pixels). Second, we propose an approach for converting reflectance ratios to the aerosol optical depth for the clear pixels. Finally, we use Monte Carlo RT calculations and 3D fields of cumulus clouds and aerosol generated by a large eddy simulation (LES) model to illustrate the
performance of the retrieval with the model-output inverse problem.
2. Aerosol Optical Depth Retrieval [4] Retrievals of t a from satellite observations consist of two basic steps: (1) sampling, which includes detection of clear pixels and (2) an algorithm, which estimates the aerosol optical depth in these pixels. The quality of the final product depends strongly on both steps [Ignatov et al., 2005]. Detection of clear pixels under cloudy conditions is discussed thoroughly by Wen et al. [2007, and references therein]. Here we discuss only the second step, namely the retrieval of t a for pixels, which have already been identified as clear. [5] Multiple scattering between clouds and aerosols results in a significant enhancement of visible illumination of clear patches. This enhancement leads to a positive bias in t a when retrieval algorithms based on plane-parallel approximation for radiative transfer are used. Cahalan et al. [2001] and Wen et al. [2001] have shown that the enhancement is largest near clouds and decreases to a positive asymptotic value, indicating that a constant correction can be applied when the cloud-free distance is large. For clear patches of cumulus fields, the 3D reflectance R3D can be expressed as R3D ðlÞ ¼ R1D ðlÞ þ DR3D ðlÞ:
Here, R(l) is the reflectance at wavelength l with the subscripts ‘‘3D’’ and ‘‘1D’’ indicating values obtained on the basis of 3D and one-dimensional (1D) RT calculations, respectively. Throughout this modeling study, R3D(l) is used as a surrogate for observations. The difference between 3D and 1D reflectances, DR3D, is the cloud-induced enhancement. Similar to R1D, DR3D is spectrally dependent [Wen et al., 2001]. The spectral features of R1D and DR3D are governed by optical properties of molecular atmosphere, aerosol and surface albedo. In contrast to R1D, DR3D is also a function of cloud optical properties. In particular, DR3D increases with cloud optical depth [Wen et al., 2007]. Since cloud optical properties are almost spectrally independent [Liou, 1992], we assume that relative enhancement DR3D(l)/R1D(l) depends only slightly on wavelength as well. In other words, we assume that DR3D(l) gR1D(l), where wavelength-independent parameter g is a function of cloud properties. As a result, we have r3D ðl1 ; l2 Þ r1D ðl1 ; l2 Þ;
1
Pacific Northwest National Laboratory, Richland, Washington, USA.
This paper is not subject to U.S. copyright. Published in 2008 by the American Geophysical Union.
ð1Þ
ð2Þ
where r(l1, l2) is the ratio of reflectances R(l1) and R(l2) at two wavelengths l1 and l2. We test this assumption in Section 3.
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Figure 1. Horizontal distribution of the LES-derived (a) aerosol optical depth and (b) cloud optical depth at wavelength 470 nm. Here and in Figure 2 white color represents values that exceed the maximal values (red colors) of the corresponding color scales. [6] Equation (2) means that the reflectance ratio is not sensitive to the 3D cloud effects and therefore can be used to estimate t a. The ratio is a function of four parameters, as it depends on two values of aerosol optical depth t a(l1) and t a(l2), and two values of the surface albedo As(l1) and As(l2). The surface albedo can be obtained from satellite [e.g., Moody et al., 2005], aircraft and surface observations [e.g., Michalsky et al., 2003, 2006]. We therefore have one known r3D(l1, l2), which is the observed reflectance ratio, and two unknowns t a(l1) and t a(l2). By selecting an additional wavelength, we obtain an open system with two observational constraints r3D(l1, l3) and r3D(l2, l3), and three unknowns t a(li), i = 1, 2, 3. Following the MODIS and Advanced Very High Resolution Radiometer (AVHRR) operational aerosol retrieval algorithms, we close the system by approximating the spectral dependence of t a using a two-parameter functional fit [e.g., Nakajima et al., 2001; Levy et al., 2007]. In this study, we assume that the spectral dependence of t a is described by a power law t a ðlÞ ¼ bla :
ð3Þ
[7] Given this assumption, we have a closed problem of two knowns and two unknowns. Once the parameters a and b are derived from the observed ratios r3D(l1, l3) and r3D(l2, l3) (section 4), Equation (3) can be used to estimate t a(l). To examine the potential for the t a(l) retrieval, we apply the LES-derived cloud and aerosol fields (section 3) as input for the model-output inverse problem (section 4).
3. LES Output and Radiative Transfer Calculations [8] To illustrate the performance of the retrieval algorithm and to evaluate Equation (2), we use model generated aerosol, cloud, and radiation fields. The 3D fields of aerosol and clouds are simulated by the Large-Eddy Simulation (LES) cloud model with size-resolved (bin) aerosol and cloud microphysics [Ovtchinnikov and Ghan, 2005]. Simulations of cumulus clouds are performed for
typical summertime conditions at the Atmospheric Radiation Measurement (ARM) Climate Research Facility (ACRF) Southern Great Plains (SGP) site using a 10 10 5 km3 domain with 50 m horizontal and 40 m vertical resolutions. For radiation calculations, the U.S. standard atmosphere with the largest altitude of 100 km [Liou, 1992] is applied above the LES domain. The aerosol and cloud optical properties are calculated based on Mie theory using droplet and aerosol size distributions predicted by the LES model. We assume that aerosol is non-absorbing, and this assumption is feasible for the SGP site [Michalsky et al., 2006]. Figure 1 shows the horizontal distribution of aerosol and cloud optical depths. The aerosol optical depth exhibits large spatial variability due to strong gradients in humidity and aerosol concentration. The values of 1D and 3D nadir reflectance at three wavelengths (l1, l2, and l3) are calculated using a Monte Carlo technique [Kassianov and Kogan, 2002], which has been validated during the International Intercomparison of 3D Radiation Codes [Cahalan et al., 2005]. We set the number of photons per pixel at 10000. Radiative transfer simulations are performed for three wavelengths l1,2,3 = 660, 870, and 470 nm, which correspond to MODIS bands 1, 2, and 3, respectively. Note, that another set of wavelengths, which provides validity of Equation (2), can be selected. Calculations are performed for a solar zenith angle of 30° and azimuth angle of 90° (direction from sun to surface is along x-axis) and typical summertime spectral values of surface albedo at the ACRF SGP site [Michalsky et al., 2006]. In particular, we assume that the surface is Lambertian with spectral values of 0.065, 0.24, and 0.04, at wavelengths l1, l2 and l3, respectively. [9] Figure 2a shows the difference between reflectances R3D(470) and R1D(470). Generally, R1D substantially overestimates the reflectance for shadowed pixels and underestimates it for other cloud-free pixels. In the presented case, R3D is 10 to 15% larger than R1D for pixels located away from clouds and their shadows (Figure 2a), consistent with the study by Wen et al. [2007]. In contrast to the reflectances R3D and R1D, the reflectance ratios r3D(660, 470)
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Figure 2. Relative difference (%) (a) between reflectances R3D and R1D at wavelength 470 nm and (b) between reflectance ratios r3D(660, 470) and r1D(660, 470). and r1D(660, 470) are very close to each other for clear pixels outside clouds and their shadows (Figure 2b). For the majority of clear pixels, the difference between 3D and 1D reflectance ratios is within 3%. Similar agreement is
obtained for the ratios r3D(870, 470) and r1D(870, 470) (not shown). This supports the validity of Equation (2), which is the main requirement for selecting wavelengths for the proposed t a retrieval. The following section provides
Figure 3. Two-dimensional diagrams of model (a, b) aerosol optical depth and (c, d) reflectance ratios in terms of the parameters a and b. Aerosol optical depth values for two wavelengths 470 nm (Figure 3a) and 870 nm (Figure 3b) are obtain from Mie calculations for aerosol model (Equation (3)). Corresponding values of the reflectance ratios for 870 and 470 nm (Figure 3c) and 660 and 470 nm (Figure 3d) are calculated using these two-dimensional diagrams of aerosol optical depth and 1D version of Monte Carlo method. 3 of 5
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Figure 4. (a) Retrieved aerosol optical depth, (b) corresponding difference between derived and true values at wavelength 470 nm, and (c) the domain-averaged values of retrieved and true aerosol optical depths for three wavelengths 470, 660, and 870 nm. The averaging is performed for clear pixels (see text for details). In Figures 4a and 4b, white color represents clouds, shadows and their adjacent clear sky area. a description of the retrieval algorithm and illustrates its performance.
4. Model Data Aerosol Retrieval [10] We start with calculation of two-dimensional lookup tables of aerosol optical depth t ab as a function of two parameters a and b (Figures 3a and 3b). These tables are created for three wavelengths (l1, l2 and l3) by using Equation (3), where a varies between 0.7 and 2.26 and b varies between 0.004 and 0.16. Corresponding values of aerosol optical depths cover wide ranges: 0.007 to 0.881 for l = 470 nm; 0.005 to 0.409 for l = 660 nm; and 0.004 to 0.219 for l = 870 nm. There is a substantial difference between the created t ab tables. For example, t ab(470) is more sensitive than t ab(870) to the parameter a, which determines the slope of the power law (Figures 3a and 3b). Then we calculate the corresponding 1D spectral reflectances at three wavelengths (l1, l2, and l3) and construct two ratios rab(l1, l3) and rab(l2, l3) (Figures 3c and 3d) by
using these t ab tables as input. It should be mentioned that ratios rab(l1, l3) and rab(l2, l3) are functions of optical properties of molecular atmosphere and surface albedo as well. For small t ab values, these properties control variations of the ratios. [11] The simulated retrieval procedure is performed by assuming that calculated ratios r3D(l1, l3) and r3D(l2, l3) represent ‘‘observations’’ and applying created look-up tables of rab(l1, l3) and rab(l2, l3) to retrieve two parameters a and b. Because isolines of constant reflectance ratios are nearly orthogonal over much of the (a, b) domain in Figures 3c and 3d, a unique solution for the (a, b) pair can be obtained except at very low b (i.e., very low aerosol optical depth). Once a and b are determined, Equation (3) gives the retrieved aerosol optical depth as a function of wavelength t a,ret(l). Figure 4 shows the results of the model-output inverse problem. For the majority of clear pixels, the difference between t a and t a,ret is within 10% (Figure 4b). Fluctuations of the retrieved t a,ret values can be partly attributed to the uncertainties in the RT calculations,
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which can be reduced by increasing the number of photons per pixel [Barker et al., 2003]. Compared to the pixel-based differences, the domain-averaged ones are much smaller (Figure 4c). [12] The aerosol retrievals are performed with 50 m horizontal resolutions. Such fine-resolution observations can be obtained from aircraft [e.g., Ovtchinnikov and Marchand, 2007] or Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) [e.g., Wen et al., 2007]. However, MODIS and Multiangle Imaging Spectroradiometer (MISR) [Kahn et al., 2005] instruments have coarser resolution (250 to 1000 m). Therefore, the sensitivity of the aerosol retrieval to imager resolution should be considered carefully and this important issue deserves further investigations.
5. Summary [13] In this study, we propose a new algorithm for retrieving aerosol optical depth in the presence of cumulus clouds, which is based on ratios of the reflectances at different wavelengths. We use Monte Carlo radiative transfer calculations and 3D LES-derived fields of cumulus clouds and aerosol to illustrate that the ratio of reflectances at 660, 870, and 470-nm channels for clear pixels are less sensitive to the 3D clouds effects than the reflectances themselves. The illustrated weak sensitivity of the ratio to the 3D clouds effects is mainly associated with weak spectral variability of cloud optical properties in the considered spectral range (400 – 900 nm). Such spectral variability suggests that the 3D cloud effects caused by surrounding clouds may be proportional at different wavelengths. Thus, the ratio of reflectances can substantially reduce the 3D cloud effects. Results of the model-inverse problem suggest that for the majority of clear pixels the error in the retrieved value of t a is within 10%, while the domain-averaged values of t can be retrieved more accurately (1%). [14] The NASA Earth Observing System (EOS) includes the MODIS, ASTER [e.g., Wen et al., 2007], and MISR [Kahn et al., 2005] instruments, which span the visible (400 – 700 nm) and near-infrared (700– 1300 nm) regions. Our preliminary study demonstrates that such EOS instruments may have the potential for accurate estimation of t a under partly cloudy conditions. The suggested approach, if proven accurate and effective, could be applied to the current and future MODIS/ASTER/MISR observations as an operational tool for t a monitoring in the vicinity of clouds. Also, the existing long-term MODIS/ASTER/MISR statistics of t a obtained in clear patches of cloud fields, which are likely to be systematically biased [Wen et al., 2007], could be improved by using the suggested approach. As a result, this approach could be considered as a potential research tool to study complex relationship between aerosols and clouds and estimate their impact on the regional and global climates. [15] Acknowledgments. This work was supported by the National Aeronautics and Space Administration (NASA) through the Radiation Sciences Program and the Office of Biological and Environmental Research (OBER) of the U.S. Department of Energy (DOE) as part of the Atmospheric Radiation Measurement (ARM) Program. The Pacific Northwest National Laboratory (PNNL) is operated for the DOE by Battelle Memorial
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Institute under contract DE-AC06-76RLO 1830. This research was performed in part using the MSCF in EMSL, a national scientific user facility sponsored by the U.S. DOE, OBER, and located at PNNL. We are grateful to anonymous reviewers for thoughtful comments.
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E. I. Kassianov and M. Ovtchinnikov, Pacific Northwest National Laboratory, 3200 Q. Avenue, MSIN: K9-24, Richland, WA 99354, USA. (
[email protected])
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