The impact of horizontal heterogeneities, cloud fraction, and liquid water path on warm cloud effective radii from CERES-like Aqua MODIS retrievals

The impact of horizontal heterogeneities, liquid water path (LWP from AMSR-E), and cloud fraction (CF) on MODIS cloud effective radius ( re), retrieved from the 2.1 μm (re2.1) and 3.8 μm ( re3.8) channels, is investigated for warm clouds over the southeast Pacific. Values of re retrieved using the CERES algorithms are averaged at the CERES footprint resolution ( ∼ 20 km), while heterogeneities ( Hσ ) are calculated as the ratio between the standard deviation and mean 0.64 μm reflectance. The value of re2.1 strongly depends on CF, with magnitudes up to 5 μm larger than those for overcast scenes, whereas re3.8 remains insensitive to CF. For cloudy scenes, bothre2.1 and re3.8 increase withHσ for any given AMSR-E LWP, butre2.1 changes more than for re3.8. Additionally, re3.8–re2.1 differences are positive ( < 1 μm) for homogeneous scenes ( Hσ < 0.2) and LWP> 45 gm−2, and negative (up to−4 μm) for largerHσ . While re3.8–re2.1 differences in homogeneous scenes are qualitatively consistent with in situ microphysical observations over the region of study, negative differences – particularly evinced in mean regional maps – are more likely to reflect the dominant bias associated with cloud heterogeneities rather than information about the cloud vertical structure. The consequences for MODIS LWP are also discussed.


Introduction
Cloud optical thickness (τ ) and effective radius (r e ) derived from visible and near-infrared satellite instruments have become the standard observational data set in cloud-atmospheric research.The availability of these parameters at high temporal and spatial resolution over the globe over long time periods makes them particularly suitable for climate studies (e.g., Stubenrauch et al., 2013).Among several practical simplifications that make the inverse problem of determining r e and τ tractable is the assumption that clouds are horizontally homogeneous (plane-parallel) objects.Nevertheless, the effect of neglecting the cloud 3-D structure and the associated radiative fields can be a significant source of retrieval error (Marshak et al., 2006).Given this uncertainty, there is an increasing interest in understanding how the 3-D radiative effects can obscure the physical insight gained from satellite observations.Multi-spectral instruments such as the MODerate resolution Imaging Spectroradiometer (MODIS) offer practical ways to explore 3-D related artifacts in the retrievals.Since 3-D radiative effects are wavelength dependent, the use of three MODIS r e retrievals from the 1.6, 2.1, and 3.8 µm channels provides a simple framework to explore biases in the observations (e.g., Zhang and Platnick, 2011).Although in principle r e retrieved at 3.8 µm is less sensitive to planeparallel biases and 3-D radiative effects, determining the effects of cloud heterogeneities with the use of multispectral r e retrievals is difficult as the different photon penetration of the three MODIS channels in theory should also capture physical information of the cloud vertical structure (Platnick, 2000).This implies that the 3.8 µm-based r e is more influenced by properties closer to the cloud top than the 2.1 and 1.6 µm counterparts.

D. Painemal et al.: The impact of horizontal heterogeneities, cloud fraction, and liquid water path
In this contribution, we explore the ways that cloud properties retrieved from Aqua MODIS radiances vary for different cloud dynamical configurations and spatial heterogeneities at spatial resolutions typical of synoptic/climate studies.The goal here is to determine the bias magnitude in r e due to heterogeneities as well as understanding the physical information that can be obtained from r e differences calculated at two wavelengths (3.8 and 2.1 µm).

Data set
Here we use values of τ and r e retrieved from Aqua MODIS data using algorithms that will be used to generate the Clouds and Earth's Radiant Energy System (CERES) Edition-4 products and averaged in the same manner as the CERES Single Scanner Footprint (SSF) product (CERES, 2012) to create a pseudo-SSF (hereafter PSSF).The Edition-4 algorithm changes relative to the CERES Edition-2 techniques (Minnis et al., 2011a) are mostly summarized by Minnis et al. (2010).The cloud parameters are derived from 1 km MODIS radiances sampled every other scan line and fourth element, and convolved with the CERES instrument point spread function to produce averages and standard deviations that match the CERES instrument footprint (∼ 20 km at nadir).The PSSF used here includes several hundred parameters including averages and standard deviations of the MODIS radiances, τ retrieved at 0.64 µm, and three r e values retrieved from the 1.2, 2.1, and 3.8 µm MODIS channels.The multispectral retrievals for r e use the same method as that described by Minnis et al. (2011) to obtain r e at 3.8 µm, r e3.8 , except that the 1.2 and 2.1 µm reflectances substitute for the 3.8 µm brightness temperatures in the iterative solution to yield r e1.2 and r e2.1 , respectively.In this investigation we only use the 3.8 and 2.1 µm-based r e , because they have proven to yield contrasting sensitivities to both the cloud vertical and horizontal structure (Platnick, 2000;Zhang and Platnick, 2011).The 1.2 µm-based r e retrieval is still experimental and will require further evaluation before being used for scientific analyses.Cloud fraction (CF) is also convolved from the clear and cloudy MODIS pixels within each CERES footprint.Although the CERES cloud algorithm differs from that of the MODIS Atmospheres team (Platnick et al., 2005), both results agree well for r e3.8 , with some small differences mainly explained by the tendency of the MODIS team Collection 5 retrievals to discard pixels with very thin clouds or near the cloud edges in broken scenes (Minnis et al., 2011b).Figure 1a shows the mean CERES r e3.8 (colors) and r e = r e3.8 -r e2.1 (contours) during the period of study.The r e3.8 values agree with MODIS team counterpart in Zhang and Platnick (2011) and Nakajima et al. (2010), in terms of magnitude and westward gradient.Moreover, as in the MODIS team retrievals, r e2.1 is generally larger than r e3.8 , with a westward increase of | r e | (Fig. 1a, contours), consistent with larger liquid water paths as well (O'Dell et al., 2008).
These features are also common to other marine stratocumulus regimes (Zhang and Platnick, 2011).
We computed a heterogeneity index H σ , defined as the ratio of the standard deviation to the mean MODIS 0.64 µm at 1 km reflectance at the PSSF resolution (∼ 20 km at nadir) using the 1 × 4 sampling of the PSSF.We note that H σ defined here differs from that in Liang et al. (2009), which was calculated at a 1 km resolution from the 250 m and 0.86 µm MODIS reflectances.While the 1 km H σ is more adequate for studying 3-D radiative effects, the use of a coarser H σ , along with spatially averaged r e , is relevant for determining how spatial heterogeneities might bias the retrievals at typical resolutions used in regional/climate studies.Our assumption here is that heterogeneities at sub-pixel scale also manifest at macroscopic scales, such as that of the CERES footprint resolution.In other words, the cloud retrievals' dependence on the CERES-scale H σ reported in this study mostly emerges from the pixels' internal variability (< 1 km).
Finally, as explained in Painemal et al. (2012), in order to create regular-grid maps, we spatially average the PSSF variables to a resolution of 0.5 • (each new grid contains at least one PSSF near the scan edge).
Independent liquid water path (LWP) retrievals are from the Advanced Microwave Scanning Radiometer-EOS, AMSR-E (Wentz and Meissner, 2000), and spatially averaged to a 0.5 • spatial resolution from the 0.25 • native resolution.In order to minimize precipitation biases in AMSR-E LWP, we limited our analysis to clouds with LWP < 150 g m −2 .While this threshold screens cases with moderate and heavy precipitation, it still allows cloud sampling with light precipitation and drizzle (e.g., Leon et al., 2008;Kubar et al., 2009;Painemal and Zuidema, 2011).
As in Zhang and Platnick (2011), our focus is on the marine stratocumulus regime of the southeast Pacific, defined here as encompassing the oceanic area within the bounds 100-70 • W and 33-5 • S. We analyze 15 months of daily satellite passes from 2002 to 2004 during the August-December period, when the cloud deck is at its maximum spatial development.The solar zenith angles between 20 • and 35 • allow us to isolate the effect of cloud heterogeneities from the solar zenith angle influence in the retrievals, especially for very oblique angles (Kato and Marshak, 2009).

Brief description of the microphysical features during VOCALS-REx
An advantage of limiting our study to the southeast Pacific Ocean is that we can exploit the improved microphysical understanding gained from the VAMOS Ocean-Cloud-Atmosphere-Land Study (VOCALS) Regional Experiment (Mechoso et al., 2013).Specifically, more than 100 cloud vertical samples over the 19-30 • S and 85-71 • W domain, collected during October-November of 2008, reveal in great detail the cloud microphysical structure of the marine stratocumulus clouds.In situ observations of westward increases in both r e and LWP were typical during VOCALS-REx, and connected with a boundary layer deepening and more drizzle occurrence.These zonal changes are qualitatively well reproduced by retrievals using MODIS data (Painemal and Minnis, 2012;Brunke et al., 2010).In terms of the vertical structure, in situ observations also yield a robust pattern, in which r e monotonically increases toward the cloud top, regardless of the magnitude of LWP (Fig. 5 in Painemal and Zuidema, 2011).Although precipitation can modify the r e profile, the droplet size tends to peak at the cloud top even for clouds with LWP as large as 250 gm −2 (Painemal and Zuidema, 2011).The cloud vertical structure observed during VOCALS-REx has interesting similarities with other field campaigns.For instance, droplet measurements in shallow cumuli collected during the Rain In Cumulus over the Ocean field experiment also evince a maximum r e near the cloud top (Arabas et al., 2009).The fact that the particle size seems to be unaffected by cloud top entrainment indicates that the mixing is mostly homogeneous.That is, the evaporation timescale is faster than the mixing scale (Lehmann et al., 2009).
In the context of MODIS satellite retrievals, if the source of difference between r e2.1 and r e3.8 arises exclusively from the cloud vertical inhomogeneity unaccounted for in the algorithm, then expectations built upon aircraft observations should be that r e3.8 > r e2.1 , as discussed in Platnick (2000).

Cloud fraction and heterogeneity
Mean H σ shows typical values between 0.1 and 0.4, with increasing heterogeneities westward (Fig. 1b).As expected, H σ and CF spatially co-vary, with a decrease in cloud fraction generally concomitant with larger H σ .The spatial similarities between r e , r e , H σ , and CF motivate a more detailed inspection of the factors that control r e .
The histogram in Fig. 2a shows that the scene heterogeneity tends to increase with CF until CF reaches 60 %.For higher CFs, H σ is anti-correlated with CF, whereas for nearly overcast scenes, the liquid water path modulates H σ , as shown in the following sections.Figure 2b and c depict the binned values of r e3.8 and r e2.1 as functions of CF and H σ .As expected, the general trend is that both r e3.8 and r e2.1 increase with H σ , reaching their largest magnitude for H σ = 0.4.Nevertheless, both retrievals show dissimilar sensitivities to changes in CF.While r e3.8 is insensitive to CF variations, r e2.1 decreases with CF, with radii between 12 and 17 µm for a fixed H σ = 0.2.It can also be seen that the r e3.8 − r e2.1 difference ( r e ) is near −6 µm for H σ < 0.15 and CF = 40 %, whereas this is reduced to around −1 to −2 µm for overcast scenes only.These results strongly support the observations made by Zhang and Platnick (2011) for a limited number of overcast and broken MODIS granules.The values of r e , as a function of CF and H σ , are in agree-ment with the smaller impact of 3-D radiative transfer and sub-pixel variability on r e3.8 than on r e2.1 , although the negligible impact of CF on r e3.8 is surprising.

Heterogeneity and AMSR-E liquid water path in cloudy scenes
For cloudy scenes, when CF > 98%, an LWP-dependent analysis is relevant because one should expect a relationship between LWP, H σ , and the cloud vertical structure.LWP has been recognized as a cloud macrophysical property (e.g., Wood, 2012), as it is the manifestation of different forcing parameters, such as sea surface temperature, divergence, humidity, and atmospheric stability (e.g., Stevens and Brenguier, 2009).LWP and in-cloud turbulence (updrafts) are linked because an LWP increase produces stronger cloud top radiative cooling, which in turn favors the turbulence production.Moreover, increasing LWP associated with boundary layer deepening (e.g., Painemal et al., 2013) should facilitate droplet size condensational growth.All these factors modify the cloud droplet activation and growth, affecting the droplet size, the vertical structure, and drizzle generation.The use of LWP as a proxy for the cloud dynamics has also been applied for isolating the cloud-aerosol interactions from those factors associated with the regional circulation and cloud dynamics (e.g., McComiskey and Feingold, 2012, and references therein).
To tackle the problem of untangling the heterogeneity bias from the physical information, we use AMSR-E LWP, a retrieval that is nearly insensitive to 3-D radiative transfer effects for the clouds investigated in this work.Similar to the approach in Sect.4, we binned the MODIS retrievals as functions of both H σ and AMSR-E LWP. Figure 3a shows the dual dependence of r e3.8 on H σ and LWP.Irrespective of H σ , r e3.8 increases with LWP, which is consistent with condensational growth and more active collision and coalescence when water content increases.In addition, r e3.8 increases with H σ are also apparent, in agreement with other studies (Zhang and Platnick, 2011).The magnitude of the change in r e3.8 with H σ is confined to 3-4 µm for any given LWP bin.
Differences between r e3.8 and r e2.1 are depicted in Fig. 3b.The largest differences, near 4 µm, are observed for the most heterogeneous cases, irrespective of LWP.For H σ = 0.1, r e is small but positive for LWP > 45 g m −2 (∼ 0.8 µm for LWP = 125 g m −2 ).This result is remarkable as it agrees with in situ observations (Sect.3) in stratocumulus clouds, for different magnitudes of in situ LWP, including light precipitating events (Painemal and Zuidema, 2011).The physical consistency between MODIS retrievals builds confidence in the utility of the cloud retrievals for representing general aspects of the cloud vertical structure within homogeneous cloud scenes.Finally, Fig. 3c shows the expected decrease of τ with increasing H σ , as well as the optical thickening with increasing LWP.

Revisiting the impact of H σ on MODIS liquid water path
Because the product of r e and τ can be used to estimate LWP, we center our focus on LWP.Here, we express the MODIS LWP by assuming a cloud having a vertical increase of water content and r e with height: where ρ w denotes the density of the liquid water.LWP in Eq (1) is 5/6 the magnitude of that calculated for a vertically homogeneous cloud, and it is adopted here because it yields better agreement with microwave estimates and in situ observations (Seethala and Horvath, 2010;Painemal et al., 2012).
Given the westward gradients in r e and H σ observed in Fig. 1, we analyze further the impact of using r e3.8 and r e2.1 in the computation of MODIS LWP (Eq.1), in the context of spatial heterogeneities.Figure 4a and b show histograms for the biases between AMSR-E and MODIS LWP, for a 4 • × 3 • coastal (centered at 76.75 • W, 23.75 • S) and offshore (centered at 97.75 • W, 23.75 • S) region, respectively.The blue histogram indicates LWP differences calculated using daily r e3.8 (LWP 3.8 ), whereas its red counterpart makes use of r e2.1 (LWP 2.1 ).Coastal histograms (Fig. 4a) show a narrow distribution, in part because LWP tends to be small near the coast.In addition, the histograms do not suggest meaningful differences between AMSR-E and MODIS retrievals, whether they are calculated with LWP 3.8 or LWP 2.1 (mean biases −7.5 and −5.6 gm −2 ).In contrast, offshore histograms (Fig. 4b) are broader, with a shift toward larger positive bias for LWP AMSR-E -LWP 3.8 relative to LWP AMSR-E -LWP 2.1 .The mean AMSR-E/MODIS biases are 9. 1.4 gm −2 for LWP 3.8 and LWP 2.1 , respectively.Interestingly, the differences between Fig. 4a and b are accompanied by contrasting changes in H σ (Fig. 4c).Coastal and offshore regions yield distinctive values of H σ , with a distribution mode of 0.15 for coastal clouds (Fig. 4c, gray line), and 0.25 for far offshore clouds (black line).The MODIS LWP and H σ relationship is further emphasized in Fig. 4d, where mean H σ values and the mean differences between LWP 3.8 and LWP 2.1 are shown as a function of longitude.The LWP 3.8 -LWP 2.1 zonal gradients are concomitant with H σ increases, indicating a distinctive bias compensation between both r e values and τ to changes in heterogeneities.We explore this idea in more detail by taking averages of all the binned MODIS variables over the study region (constructed from LWP AMSR-E ) as a function of H σ bins.The results in Fig. 5a reveal a close match between r e2.1 and r e3.8 for homogeneous cases and a greater increase of r e2.1 with H σ (black and red lines).The decreases in MODIS LWP with H σ in Fig. 5b are more dramatic for LWP 3.8 .Here, the AMSR-E LWP is constant at 80 g m −2 by design.We quantify the influence of H σ by analyzing fractional changes of MODIS LWP relative to fractional changes in H σ , ∂ ln(LWP κ ) ∂ ln(H σ ) , with κ = 3.8, 2.1.It follows from Eq. (1) that

Atmos
where m LWP, κ , m rκ , and m τ in Eq. ( 2) are calculated as the slopes of the natural logarithm of the curves in Fig. 5a

Conclusions
Motivated by studies that support both the physical and the 3-D radiative interpretation of the differences in r e values derived from the 3.8 and 2.1 µm MODIS data, we endeavored to understand the contribution of LWP and H σ to the r e variability.Homogeneous clouds have larger values of r e3.8 relative to r e2.1 , indicating a physical increase of r e toward the cloud top and a negligible effect of precipitation in the retrievals.Our results are consistent with aircraft observations of cloud microphysics over the region of study, which show an adiabatic-like cloud behavior (Painemal and Zuidema, 2011).The current study also shows that the use of r e for microphysical studies without knowledge of H σ is insufficient for determining vertical features of the cloud.Moreover, because H σ is typically large in cumulus clouds, they will continue to pose a formidable challenge for passive remote sensing.Overall, we conclude that r e is more suitable as a metric to investigate cloud heterogeneities rather than the cloud physical structure in marine stratocumulus clouds.
A result of interest for cloud-aerosol interaction studies is the lack of sensitivity of r e3.8 to CF.Although a weaker dependence of r e3.8 on CF is expected from the reduced photon vertical penetration at 3.8 µm and from the smaller sensitivity to sub-pixel variability (plane-parallel bias) than retrievals at 2.1 µm, the negligible dependence of r e3.8 on CF is rather unexpected.We hypothesize that this is related to the fact that our observations are 0.5 • × 0.5 • averages, which allow further error cancellation (e.g., Marshak et al., 2006).We recommend caution when using r e2.1 combined with nearly collocated aerosol optical thickness, especially if broken clouds dominate the r e retrieval scenes.A similar problem might arise if variability in r e2.1 is analyzed as a function of meteorological factors, since they are likely to be correlated with cloud cover variability (e.g., Lebsock et al., 2008).
The problem of determining errors in MODIS-based LWP is difficult because of the dissimilar responses of r e and τ to changes in cloud heterogeneities.Our results also provide interpretation of the AMSR-MODIS LWP bias correlation with www.atmos-chem-phys.net/13/9997/2013/r e reported by Seethala and Horvath (2010).The smaller values of MODIS LWP relative to the AMSR-E values, when r e2.1 greatly exceeds r e3.8 , are associated with the rapid decrease of τ with H σ (relative to homogeneous scenes with the same AMSR-E LWP) that tends to occur with rising AMSR-E LWP.It is still puzzling why the MODIS LWP is slightly larger than AMSR-E LWP for highly homogeneous cases.A plausible cause might be linked to the thermal emission underestimation within the AMSR-E LWP algorithm (Seethala and Horvath, 2010), although unexplained overestimates of MODIS r e relative to in situ observations (Painemal and Zuidema, 2011) might also contribute to overestimates of MODIS LWP relative to AMSR-E LWP.
Finally, while this analysis is only valid for clouds with LWP < 150 gm −2 , our results can help by determining the minimum thresholds by which r e3.8 -r e2.1 differences might potentially indicate physical information about the cloud vertical structure.As suggested by Figs.5a and 3b, we speculate that r e differences in cloudy scenes must at least surpass |−4.0 µm| (the largest differences for the most heterogeneous scenes) to be plausibly considered as physical rather than biases due to sub-pixel variability.This threshold would imply that, on average, values of r e2.1 exceeding 18 µm over oceanic regions (Fig. 3 in Nagao et al., 2013) along with r e2.1 > (r e3.8 + 4 µm) might be indicative of the actual effect of precipitation on r e , which would tend to increase droplet size toward the cloud base.