Implications of MODIS bow-tie distortion on aerosol optical depth retrievals, and techniques for mitigation

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Atmos. Meas. Tech., 8, 5277–5288, 2015 doi:10.5194/amt-8-5277-2015 © Author(s) 2015. CC Attribution 3.0 License. Implications of MODIS bow-tie distortion on aerosol optical depth retrievals, and techniques for mitigation A. M. Sayer1,2, N. C. Hsu1, and C. Bettenhausen1,3 1NASA Goddard Space Flight Center, Greenbelt, Maryland, USA 2Goddard Earth Sciences Technology And Research (GESTAR), Universities Space Research Association (USRA), Columbia, Maryland, USA 3Science Systems and Applications Inc., Lanham, Maryland, USA Correspondence to: A. M. Sayer ( Received: 20 July 2015 – Published in Atmos. Meas. Tech. Discuss.: 18 August 2015 Revised: 4 December 2015 – Accepted: 7 December 2015 – Published: 17 December 2015 Abstract. The scan geometry of the Moderate Resolution Imaging Spectroradiometer (MODIS) sensors, combined with the Earth’s curvature, results in a pixel shape distortion known as the “bow-tie effect”. Specifically, sensor pixels near the edge of the swath are elongated along-track and across-track compared to pixels near the centre of the swath, resulting in an increase of pixel area by up to a factor of ∼ 9 and, additionally, the overlap of pixels acquired from consecutive scans. The Deep Blue and Dark Target aerosol optical depth (AOD) retrieval algorithms aggregate sensor pixels and provide level 2 (L2) AOD at a nominal horizontal pixel size of 10 km, but the bow-tie distortion means that they also suffer from this size increase and overlap. This means that the spatial characteristics of the data vary as a function of satellite viewing zenith angle (VZA) and, for VZA > 30 , corresponding to approximately 50 % of the data, are areally enlarged by a factor of 50 % or more compared to this nominal pixel area and are not spatially independent of each other. This has implications for retrieval uncertainty and aggregated statistics, causing a narrowing of AOD distributions near the edge of the swath, as well as for data comparability from the application of similar algorithms to sensors without this level of bow-tie distortion. Additionally, the pixel overlap is not obvious to users of the L2 aerosol products because only pixel centres, not boundaries, are provided within the L2 products. A two-step procedure is proposed to mitigate the effects of this distortion on the MODIS aerosol products. The first (simple) step involves changing the order in which pixels are aggregated in L2 processing to reflect geographical location rather than scan order, which removes the bulk of the overlap between L2 pixels and slows the rate of growth of L2 pixel size vs. VZA. This can be achieved without significant changes to existing MODIS processing algorithms. The second step involves additionally changing the number of sensor pixels aggregated across-track as a function of VZA, which preserves L2 pixel size at around 10 km × 10 km across the whole swath but would require algorithmic quality assurance tests to be re-evaluated. Both of these steps also improve the extent to which the pixel locations a user would infer from the L2 data products represent the actual spatial extent of the L2 pixels. 1 Introduction The Moderate Resolution Imaging Spectroradiometers (MODIS) aboard the Terra and Aqua platforms have been used to create data products for a range of earth science disciplines, including analyses of the atmospheric aerosol burden. Mid-visible aerosol optical depth (AOD) data products have been generated routinely by a variety of dedicated algorithms over bright (Hsu et al., 2004, 2006, 2013) and dark (Kaufman et al., 1997; Levy et al., 2007, 2013; Hsu et al., 2013) land surfaces, ocean surfaces (Tanré et al., 1997; Levy et al., 2013), and as a by-product of algorithms for the atmospheric correction of land/ocean surface reflectance (e.g. Ahmad et al., 2010; Lyapustin et al., 2011). The level 2 (L2; orbit-level) MODIS dedicated aerosol data product is known as MOD04 for data generated from MODIS Terra and MYD04 for data from MODIS Published by Copernicus Publications on behalf of the European Geosciences Union. 5278 A. M. Sayer et al.: MODIS bow-tie effect and aerosols Aqua (hereafter MXD04 collectively). The latest version of MXD04 products (Collection 6, C6) contains data generated by the Deep Blue (DB) algorithms over land surfaces (Hsu et al., 2013), a Dark Target (DT) over-land algorithm, and an over-water algorithm which also uses wavelengths at which the water surface is dark (Levy et al., 2013). These L2 products are generated from level 1b (L1b) calibrated radiance data measured by the MODIS instruments. To decrease noise in the retrieval and provide a manageable data volume, the standard L2 products are provided at a nominal horizontal pixel size of 10 km (referred to as “retrieval pixels”) compared to a L1b pixel size of 0.25–1 km (dependent on band, referred to as “sensor pixels”). As aerosol horizontal variations are often on length scales of the order of tens of kilometres (e.g. Anderson et al., 2003), this pixel size should preserve the underlying spatial shape of aerosol fields without major smoothing of features. Note that a separate nominal 3 km DT product is also available, albeit with larger uncertainties than the 10 km standard product (Munchak et al., 2013; Remer et al., 2013, Livingston et al., 2014). However, a consequence of the MODIS scan geometry and Earth’s curvature, of which many users of MXD04 data may not be aware, is a distortion of pixel size and shape from the centre to the edge of the swath. This is known as the “bow-tie effect” and has the potential to alias into angledependent artefacts and changes in retrieval quality in the derived data sets. It also presents a challenge for the continuation of MODIS-like data sets using similar sensors such as the Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar-orbiting Partnership (S-NPP) platform, launched in late 2011, for which these bow-tie distortions are much smaller. Consequently, data sets generated from similar algorithms may exhibit different angulardependent characteristics. The purpose of this study is to illustrate the influence of the MODIS bow-tie distortion on AOD retrievals and examine some techniques for mitigation of these distortions, for potential application in future MODIS (or VIIRS) data reprocessings. Section 2 discusses MODIS and its scan geometry, providing an illustration of the bow-tie effect and the dependence of MODIS AOD retrievals on view angle. Section 3 proposes a two-step solution to mitigate these effects, of which the first step is relatively simple and could be accomplished with minor changes to existing MODIS processing algorithms, while the second step would require more careful evaluation. Finally, Sect. 4 provides a discussion on the importance of the results. 2 Illustration of the problem MODIS takes measurements in a total of 36 bands with central wavelengths between 412 nm and 14.4 µm (Barnes et al., 1998; Toller et al., 2013). The L1b data are organised into 5 min granules, which consist of 1354 pixels across-track and 203 scans along-track. The term “along-track” indicates the One scan Sub-satellite track Along-track Across-track (2,330 km swath) Figure 1. Illustration of some terms related to MODIS scan geometry. direction of the satellite flight track (for daytime data this is approximately from north to south for Terra and from south to north for Aqua, due to the satellites’ ∼ 98.2 inclination), while “across-track” indicates the direction perpendicular to the flight track (alternating east–west and west–east for successive scans). This is illustrated in Fig. 1. Each scan is approximately 10 km wide at nadir; there are 10 detectors for nominal 1 km bands, 20 detectors for 0.5 km bands, and 40 detectors for the two bands at nominal 0.25 km resolution. Note that these quoted nominal pixel sizes are only approximate, and this terminology is used for simplicity of understanding. Barnes et al. (1998) and Xiong et al. (2006) provide more details about MODIS spatial characterisation. The MODIS spatial response functions on a pixel level are not exactly square and have some slight blurring between adjacent pixels. For example, pre-launch characterisation of MODIS Terra revealed band 8 (centred near 412 nm), nominally of 1 km pixel size, had an effective across-track size around 1.08 km across-track and 1.01 km along-track. Distortions are band dependent and, for the bands relevant to AOD retrieval, of similar (fairly small) magnitude. In the present study pixel sizes (lengths) are approximated as half the distance between adjacent pixel centres in each direction. The error introduced by this approximation is much smaller than the distortion of pixel shape/size resulting from the bowtie effect. Still it is worth bearing in mind that the representation of sensor pixels (and coarser-resolution L2 data) as quadrilaterals is an idealisation. Campagnolo and Montano (2014) provide some more discussion and on-orbit characterisation of MODIS’s spatial performance from the point of view of land surface reflectance data products. In the L1b products, the data are available both at native resolution and aggregated to the footprints of the coarser bands. For example, MODIS bands 1 and 2, centred near 650 and 860 nm respectively, are recorded with a nominal 0.25 km pixel size; however, they are additionally provided aggregated to the footprints of the 0.5 km bands (which is native resolution for bands 3–7) and 1 km bands (which is Atmos. Meas. Tech., 8, 5277–5288, 2015 A. M. Sayer et al.: MODIS bow-tie effect and aerosols 5279 Figure 2. MODIS granule used as a case study throughout this manuscript. Panel (a) shows a true-colour composite, (b) the VZA along and across the scans, (c) the L2 (nominal 10 km) Deep Blue retrieved AOD for the granule, and (d) the Deep Blue retrieval-pixel area. Effective pixel area, km2 Cumulative fraction (a) MODIS pixel growth vs. view angle 10 8 6 4 2 0 -70 -50 -30 -10 10 30 50 Viewing zenith angle, degrees 70 (b) View zenith angle histogram 1.0 0.8 0.6 0.4 0.2 0.0 0 10 20 30 40 50 60 70 Absolute viewing zenith angle, degrees Figure 3. (a) Area of nominal 1 km × 1 km sensor pixels as a function of VZA, and (b) histogram of absolute VZA. The median is shown with a dashed line. Data for the MODIS granule shown in Fig. 2. native resolution for bands 8–36). DB uses the L1b data aggregated to 1 km while the DT algorithms use the L1b data at 0.5 km. The L2 aerosol products are created by aggregating blocks of contiguous sensor pixels through one scan along-track and 10 1 km sensor pixels across-track (or 20 0.5 km pixels for the appropriate bands in DT). The DB algorithms (Hsu et al., 2013) retrieve AOD from suitable (e.g. cloud-free snow-free) data at sensor-pixel resolution and then aggregate to retrieval-pixel resolution (a “retrieve-then-average” technique), while the DT algorithms (Levy et al., 2013) average measured reflectance from suitable pixels and then perform a single retrieval at retrieval-pixel resolution (an “averagethen-retrieve” technique). The two averaging methods should be equivalent when the underlying scene is homogeneous but not when there is surface or atmospheric heterogeneity. Thus, the L2 aerosol products consist of 135 retrievalpixel positions across-track and 203 along-track (the four excess across-track nominal 1 km sensor pixels are discarded as 1354 does not divide evenly by 10). As the sensor scans across-track back and forth, the light observed by MODIS is reflected from a scan mirror onto the focal plane assemblies. Dependent on the scan direction, both sides of this scan mirror are used. Differences in the quality of the characterisation of these two mirror sides can lead to striping in the data between forward and reverse scans in some situations (Franz et al., 2007). Because of this scan geometry the spatial resolution degrades from nadir (viewing zenith angle (VZA) 0 ) to the scan edge (VZA ∼ 65 ), such that pixels near the edge of the scan are larger than those near nadir; the swath width is ∼ 2330 km, despite the fact that there are only 1354 acrosstrack sensor pixels. The primary distortion is across-track (i.e. pixels get longer in the longitudinal direction) but there is also an along-track (i.e. latitudinal) distortion, resulting in overlap between pixels from consecutive scans near the swath edges. These give a scan a shape similar to a bow tie, hence the term “bow-tie effect”. These effects are illustrated for an example MODIS Terra granule in Figs. 2 and 3. This granule is the basis for most of the results shown in this study. Note that slight asymmetries and discontinuities in the retrieval-pixel size result because of variations in terrain elevation across the granule. Although the nominal 10 km × 10 km horizontal resolution Atmos. Meas. Tech., 8, 5277–5288, 2015 5280 A. M. Sayer et al.: MODIS bow-tie effect and aerosols (a) MODIS actual nominal 1/10 km pixels, odd scans 29.5 29.4 Latitude, degrees 29.3 29.2 29.1 -5 29.5 -4 -3 Longitude, degrees (b) MODIS actual nominal 1/10 km pixels, even scans -2 29.4 Latitude, degrees 29.3 29.2 29.1 -5 29.5 -4 -3 Longitude, degrees (c) MODIS actual nominal 1/10 km pixels, all scans -2 29.4 Latitude, degrees 29.3 29.2 29.1 -5 -4 -3 Longitude, degrees -2 Figure 4. Borders of nominal 1 km sensor pixels (pale colours) and nominal 10 km retrieval pixels (strong colours) along the western edge of the granule shown in Fig. 2, illustrating the overlap between scans near swath edges. Data from alternating forward/backward scans are shown in red and blue. Panel (a) shows odd-numbered scans only, (b) even-numbered scans only, and (c) all scans. results in a retrieval-pixel area of ∼ 100 km2 near the centre of the swath, as the VZA increases, the pixel area is increased by almost a factor of 10 at the extreme edges of the swath. Figure 3 shows that the median absolute VZA is about 30 , for which pixel area is increased by around ∼ 50 % compared with VZA = 0 . Hence, although the MODIS aerosol retrieval-pixel size is commonly stated to be 10 km × 10 km, half the time the actual area encompassed by these retrieval pixels is at least 50 % larger than that. Note that the sign of VZA in Fig. 3 is defined such that positive values are found on the western side of the swath. Taking a closer view of the area near the western edge of the swath, Fig. 4 shows the ground locations of the sensor and retrieval pixels. Scans are coloured alternating in red and blue (odd scans in red, even in blue). Two factors are immediately apparent. One is the strong elongation of pixels in the across-track (longitudinal) direction. The second is that, at the swath edge, successive scans (e.g. a red-coloured scan and the blue-coloured scans immediately before and after it) are fully overlapped in the along-track direction. Each edgeof-swath retrieval covers half of the area of the retrieval pixel from the scan before it and half of the area from the scan after it (i.e. they are fully overlapping). Even 10 retrievals in from the scan edge the retrieval pixels are more than half overlapped between successive scans. This therefore represents a sizeable fraction of the MXD04 data, particularly in terms of area covered. This overlap is not obvious to L2 data product users, as the L2 files only present the central latitudes and longitudes for the retrieval pixels. Figure 5 shows the same retrievalpixel locations as in Fig. 4, except with the retrieval-pixel boundaries which would be inferred from the L2 central Atmos. Meas. Tech., 8, 5277–5288, 2015 A. M. Sayer et al.: MODIS bow-tie effect and aerosols 5281 MODIS actual and apparent (L2) 10 km pixels 29.5 29.4 Latitude, degrees 29.3 29.2 29.1 -5 -4 -3 Longitude, degrees -2 Figure 5. Borders of nominal 10 km retrieval pixels (strong colours, as in Fig. 4c) along the western edge of the granule shown in Fig. 2. Pixel centres are overplotted with coloured asterisks, and inferred L2 pixel bounds are drawn in black lines. Fraction of data 1.0000 0.1000 0.0100 0.0010 0.0001 0.0 1.0000 0.1000 0.0100 0.0010 0.0001 0.0 (a) Deep Blue arid VZA<10o VZA>55o 0.2 0.4 0.6 550 nm AOD 0.8 (c) Dark Target land 1.0 0.2 0.4 0.6 0.8 1.0 550 nm AOD Fraction of data Fraction of data 1.0000 0.1000 0.0100 0.0010 0.0001 0.0 1.0000 0.1000 0.0100 0.0010 0.0001 0.0 (b) Deep Blue vegetated 0.2 0.4 0.6 550 nm AOD 0.8 (d) Dark Target ocean 0.2 0.4 0.6 550 nm AOD 0.8 1.0 1.0 Fraction of data Figure 6. Histograms of retrieved MODIS Aqua AOD at 550 nm during the year 2006 retrieved from (a) DB over bright arid surfaces, (b) DB over dark vegetated surfaces, (c) DT over dark vegetated surfaces, and (d) the over-water DT algorithm. latitudes/longitudes overplotted. The fact that the L2 pixels overlap and are oversampled is not clear from the L2 products alone and would require auxiliary knowledge of the L1b sensor-pixel locations, which are not provided in the L2 products. All other things being equal, the expected effects of both aspects of this distortion (i.e. pixel enlargement and overlap) on the MXD04 products would be to decrease the variability of the retrieved AOD near the edge of the scan compared to that near the centre of the scan. Figure 6 shows histograms of AOD at 550 nm from all four algorithm/surface types included within the C6 MXD04 products (DB over arid and vegetated surfaces; DT over land and ocean), for data with VZA < 10 and VZA > 55 , corresponding to roughly the lowest and equilibrium value of MeCpG steps (,+14 deg.) [31,44]. In comparison, methylation has a significantly lower stability cost when happening at major groove positions, such as 211 and 21 base pair from dyad (mutations 9 and 12), where the roll of the nucleosome bound conformation (+10 deg.) is more compatible with the equilibrium geometry of MeCpG steps. The nucleosome destabilizing effect of cytosine methylation increases with the number of methylated cytosines, following the same position dependence as the single methylations. The multiple-methylation case reveals that each major groove meth- PLOS Computational Biology | 3 November 2013 | Volume 9 | Issue 11 | e1003354 DNA Methylation and Nucleosome Positioning ylation destabilizes the nucleosome by around 1 kJ/mol (close to the average estimate of 2 kJ/mol obtained for from individual methylation studies), while each minor groove methylation destabilizes it by up to 5 kJ/mol (average free energy as single mutation is around 6 kJ/mol). This energetic position-dependence is the reverse of what was observed in a recent FRET/SAXS study [30]. The differences can be attributed to the use of different ionic conditions and different sequences: a modified Widom-601 sequence of 157 bp, which already contains multiple CpG steps in mixed orientations, and which could assume different positioning due to the introduction of new CpG steps and by effect of the methylation. The analysis of our trajectories reveals a larger root mean square deviation (RMSD) and fluctuation (RMSF; see Figures S2– S3 in Text S1) for the methylated nucleosomes, but failed to detect any systematic change in DNA geometry or in intermolecular DNA-histone energy related to methylation (Fig. S1B, S1C, S4–S6 in Text S1). The hydrophobic effect should favor orientation of the methyl group out from the solvent but this effect alone is not likely to justify the positional dependent stability changes in Figure 2, as the differential solvation of the methyl groups in the bound and unbound states is only in the order of a fraction of a water molecule (Figure S5 in Text S1). We find however, a reasonable correlation between methylation-induced changes in hydrogen bond and stacking interactions of the bases and the change in nucleosome stability (see Figure S6 in Text S1). This finding suggests that methylation-induced nucleosome destabilization is related to the poorer ability of methylated DNA to fit into the required conformation for DNA in a nucleosome. Changes in the elastic deformation energy between methylated and un-methylated DNA correlate with nucleosomal differential binding free energies To further analyze the idea that methylation-induced nucleosome destabilization is connected to a worse fit of methylated DNA into the required nucleosome-bound conformation, we computed the elastic energy of the nucleosomal DNA using a harmonic deformation method [36,37,44]. This method provides a rough estimate of the energy required to deform a DNA fiber to adopt the super helical conformation in the nucleosome (full details in Suppl. Information Text S1). As shown in Figure 2, there is an evident correlation between the increase that methylation produces in the elastic deformation energy (DDE def.) and the free energy variation (DDG bind.) computed from MD/TI calculations. Clearly, methylation increases the stiffness of the CpG step [31], raising the energy cost required to wrap DNA around the histone octamers. This extra energy cost will be smaller in regions of high positive roll (naked DNA MeCpG steps have a higher roll than CpG steps [31]) than in regions of high negative roll. Thus, simple elastic considerations explain why methylation is better tolerated when the DNA faces the histones through the major groove (where positive roll is required) that when it faces histones through the minor groove (where negative roll is required). Nucleosome methylation can give rise to nucleosome repositioning We have established that methylation affects the wrapping of DNA in nucleosomes, but how does this translate into chromatin structure? As noted above, accumulation of minor groove methylations strongly destabilizes the nucleosome, and could trigger nucleosome unfolding, or notable changes in positioning or phasing of DNA around the histone core. While accumulation of methylations might be well tolerated if placed in favorable positions, accumulation in unfavorable positions would destabilize the nucleosome, which might trigger changes in chromatin structure. Chromatin could in fact react in two different ways in response to significant levels of methylation in unfavorable positions: i) the DNA could either detach from the histone core, leading to nucleosome eviction or nucleosome repositioning, or ii) the DNA could rotate around the histone core, changing its phase to place MeCpG steps in favorable positions. Both effects are anticipated to alter DNA accessibility and impact gene expression regulation. The sub-microsecond time scale of our MD trajectories of methylated DNAs bound to nucleosomes is not large enough to capture these effects, but clear trends are visible in cases of multiple mutations occurring in unfavorable positions, where unmethylated and methylated DNA sequences are out of phase by around 28 degrees (Figure S7 in Text S1). Due to this repositioning, large or small, DNA could move and the nucleosome structure could assume a more compact and distorted conformation, as detected by Lee and Lee [29], or a slightly open conformation as found in Jimenez-Useche et al. [30]. Using the harmonic deformation method, we additionally predicted the change in stability induced by cytosine methylation for millions of different nucleosomal DNA sequences. Consistently with our calculations, we used two extreme scenarios to prepare our DNA sequences (see Fig. 3): i) all positions where the minor grooves contact the histone core are occupied by CpG steps, and ii) all positions where the major grooves contact the histone core are occupied by CpG steps. We then computed the elastic energy required to wrap the DNA around the histone proteins in unmethylated and methylated states, and, as expected, observed that methylation disfavors DNA wrapping (Figure 3A). We have rescaled the elastic energy differences with a factor of 0.23 to match the DDG prediction in figure 2B. In agreement with the rest of our results, our analysis confirms that the effect of methylation is position-dependent. In fact, the overall difference between the two extreme methylation scenarios (all-in-minor vs all-in-major) is larger than 60 kJ/mol, the average difference being around 15 kJ/ mol. We have also computed the elastic energy differences for a million sequences with CpG/MeCpG steps positioned at all possible intermediate locations with respect to the position (figure 3B). The large differences between the extreme cases can induce rotations of DNA around the histone core, shifting its phase to allow the placement of the methylated CpG steps facing the histones through the major groove. It is illustrative to compare the magnitude of CpG methylation penalty with sequence dependent differences. Since there are roughly 1.5e88 possible 147 base pairs long sequence combinations (i.e., (4n+4(n/2))/2, n = 147), it is unfeasible to calculate all the possible sequence effects. However, using our elastic model we can provide a range of values based on a reasonably large number of samples. If we consider all possible nucleosomal sequences in the yeast genome (around 12 Mbp), the energy difference between the best and the worst sequence that could form a nucleosome is 0.7 kj/mol per base (a minimum of 1 kJ/mol and maximum of around 1.7 kJ/mol per base, the first best and the last worst sequences are displayed in Table S3 in Text S1). We repeated the same calculation for one million random sequences and we obtained equivalent results. Placing one CpG step every helical turn gives an average energetic difference between minor groove and major groove methylation of 15 kJ/ mol, which translates into ,0.5 kJ/mol per methyl group, 2 kJ/ mol per base for the largest effects. Considering that not all nucleosome base pair steps are likely to be CpG steps, we can conclude that the balance between the destabilization due to CpG methylation and sequence repositioning will depend on the PLOS Computational Biology | 4 November 2013 | Volume 9 | Issue 11 | e1003354 DNA Methylation and Nucleosome Positioning Figure 3. Methylated and non-methylated DNA elastic deformation energies. (A) Distribution of deformation energies for 147 bplong random DNA sequences with CpG steps positioned every 10 base steps (one helical turn) in minor (red and dark red) and major (light and dark blue) grooves respectively. The energy values were rescaled by the slope of a best-fit straight line of figure 2, which is 0.23, to source of circulating FGF-21. The lack of association between circulating and muscle-expressed FGF-21 also suggests that muscle FGF-21 primarily works in a local manner regulating glucose metabolism in the muscle and/or signals to the adipose tissue in close contact to the muscle. Our study has some limitations. The number of subjects is small and some correlations could have been significant with greater statistical power. Another aspect is that protein levels of FGF-21 were not determined in the muscles extracts, consequently we cannot be sure the increase in FGF-21 mRNA is followed by increased protein expression. In conclusion, we show that FGF-21 mRNA is increased in skeletal muscle in HIV patients and that FGF-21 mRNA in muscle correlates to whole-body (primarily reflecting muscle) insulin resistance. These findings add to the evidence that FGF-21 is a myokine and that muscle FGF-21 might primarily work in an autocrine manner. Acknowledgments We thank the subjects for their participation in this study. 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