Estimations of Global Shortwave Direct Aerosol Radiative Effects Above Opaque Water Clouds Using a Combination of A-Train Satellite Sensors

Abstract. All-sky direct aerosol radiative effects (DARE) play a significant
yet still uncertain role in climate. This is partly due to poorly quantified
radiative properties of aerosol above clouds (AAC). We compute global
estimates of shortwave top-of-atmosphere DARE over opaque water clouds
(OWCs), DAREOWC, using observation-based aerosol and cloud radiative
properties from a combination of A-Train satellite sensors and a radiative
transfer model. There are three major differences between our
DAREOWC calculations and previous studies: (1) we use the
depolarization ratio method (DR) on CALIOP (Cloud–Aerosol Lidar with
Orthogonal Polarization) Level 1 measurements to compute the AAC frequencies
of occurrence and the AAC aerosol optical depths (AODs), thus introducing
fewer uncertainties compared to using the CALIOP standard product; (2) we
apply our calculations globally, instead of focusing exclusively on regional
AAC “hotspots” such as the southeast Atlantic; and (3) instead of the
traditional look-up table approach, we use a combination of satellite-based
sensors to obtain AAC intensive radiative properties. Our results agree with
previous findings on the dominant locations of AAC (south and northeast
Pacific, tropical and southeast Atlantic, northern Indian Ocean and northwest Pacific), the season of maximum occurrence and aerosol optical depths (a
majority in the 0.01–0.02 range and that can exceed 0.2 at 532 nm) across the globe. We find positive averages of global seasonal DAREOWC between
0.13 and 0.26 W m−2 (i.e., a warming effect on climate). Regional
seasonal DAREOWC values range from −0.06 W m−2 in the
Indian Ocean offshore from western Australia (in March–April–May) to
2.87 W m−2 in the southeast Atlantic (in
September–October–November). High positive values are usually paired with
high aerosol optical depths (>0.1) and low single scattering albedos (<0.94), representative of, for example, biomass burning aerosols. Because we use
different spatial domains, temporal periods, satellite sensors, detection
methods and/or associated uncertainties, the DAREOWC estimates in
this study are not directly comparable to previous peer-reviewed results.
Despite these differences, we emphasize that the DAREOWC estimates
derived in this study are generally higher than previously reported. The
primary reasons for our higher estimates are (i) the possible underestimate
of the number of dust-dominated AAC cases in our study; (ii) our use of Level
1 CALIOP products (instead of CALIOP Level 2 products in previous studies)
for the detection and quantification of AAC aerosol optical depths, which
leads to larger estimates of AOD above OWC; and (iii) our use of gridded
4∘×5∘ seasonal means of aerosol and cloud properties in our
DAREOWC calculations instead of simultaneously derived aerosol and
cloud properties from a combination of A-Train satellite sensors. Each of
these areas is explored in depth with detailed discussions that explain both
the rationale for our specific approach and the subsequent ramifications for our
DARE calculations.


study are generally higher than previously reported. The primary reasons for our higher estimates are (i) 48 the possible underestimate of the number of dust-dominated AAC cases in our study; (ii) our use of 49 Level 1 CALIOP products (instead of CALIOP Level 2 products in previous studies) for the detection 50 and quantification of AAC aerosol optical depths, which leads to larger estimates of AOD above OWC; 51 and (iii) our use of gridded 4ºx5º seasonal means of aerosol and cloud properties in our DAREOWC 52 calculations instead of simultaneously derived aerosol and cloud properties from a combination of A-53 Train satellite sensors. Each of these areas is explored in depth with detailed discussions that explain 54 both rationale for our specific approach and the subsequent ramifications for our DARE

Introduction 60
The Direct Aerosol Radiative Effect (DARE) is defined as the change in the upwelling radiative flux 61 DAREcloudy results that use satellite observations in the literature, together with assumptions in their 80 calculations. Compared to the peer-reviewed studies of Table 1, Table 1). Second, our 84 results use a combination of A-Train satellite sensors (i.e., MODIS-OMI-CALIOP), instead of the 85 Look-Up- Table (LUT) approach used in the other studies of Table 1, to obtain estimates of the intensive 86 aerosol radiative properties above clouds. Third, the peer-reviewed global DAREcloudy calculations in 87 Table 1  ]. In our case, we estimate DAREcloudy globally by using an alternate method applied to CALIOP 91 Level 1 measurements [Hu et al., 2007b;Chand et al., 2008;Liu et al., 2015] to obtain AAC AOD and 92 the AAC frequency of occurrence. In the sections below, we explain why we have used such a method, 93 instead of other passive or active satellite sensor techniques. 94 (i.e. they impose fixed COD, Re, AOD, aerosol radiative properties, and aerosol / cloud vertical 97 distribution) and the study by Costantino and Bréon et al. [2013] (their method uses MODIS-derived 98 cloud microphysics that are not corrected for overlying aerosols). When not specified, the study uses the 99 standard CALIOP data product; otherwise, it uses the DR (Depolarization Ratio) or CR (Color Ratio) 100 The brightening of clear patches near clouds [Wen et al., 2007] (i.e., "3-D cloud radiative effect" or 119 "cloud adjacency effect") can introduce biases into the current passive satellite AAC retrieval 120 techniques (i.e., lines 1-11 of Table 2). To minimize these biases, this study relies primarily on CALIOP 121 observations [Winker et al., 2009]. CALIOP is a three-channel elastic backscatter lidar with a narrow 122 field of view and a narrow source of illuminating radiation, which limits cloud adjacency effects and the 123 subsequent cloud contamination of aerosol data products [Zhang et al., 2005;Wen et al., 2007;Várnai 124 and Marshak, 2009]. CALIOP measures high-resolution (1/3 km in the horizontal and 30m in the 125 vertical in low and middle troposphere) profiles of the attenuated backscatter from aerosols and clouds 126 at visible (532 nm) and near-infrared (1064 nm) wavelengths along with polarized backscatter in the 127 visible channel [Hunt et al., 2009]. These data are distributed as part of the Level 1 CALIOP products. 128 The Level 2 products are derived from the Level 1 products using a succession of sophisticated retrieval 129 algorithms [Winker et al., 2009]. The Level 2 processing is composed of a feature detection scheme 130 [Vaughan et al., 2009], a module that classifies features according to layer type (i.e., cloud versus 131 aerosol)  and subtype (i.e., aerosol species) [Omar et al., 2009], and, finally, an 132 extinction retrieval algorithm [Young and Vaughan, 2009] that retrieves profiles of aerosol backscatter 133 and extinction coefficients and the total column AOD based on modeled values of the extinction-to-134 In this study, we use the DR method and a combination of CALIOP Level 1 and Level 2 data products 154 to compute global estimates of the AAC frequency of occurrence (i.e., fAAC), the AAC AOD (i.e., 155 t DR AAC) and the AAC extinction-to-backscatter ratios (i.e., SAAC) (section 2.1). We then use CALIOP 156 results of fAAC, t DR AAC and other A-Train satellite products to compute global DAREcloudy (section 2.2). 157 Section 3 describes the geographical and seasonal distribution of global fAAC (section 3.1), t DR AAC and 158 SAAC (section 3.2) and DAREcloudy results (section 3.3). Section 4 revisits some of the limitations in the 159 method and proposes ways to improve on these DAREcloudy calculations. 160

AAC optical depth and extinction-to-backscatter 162
The DR method can also be called the "constrained opaque water cloud method"  as it 163 uses Opaque Water Clouds (OWCs) as reflectivity targets. The OWCs in this study are selected using 164 the five criteria listed in Table B2 of the appendix. Most importantly, (1) only one cloud can be detected 165 within a 5 km (15 shot) along-track average (which means, for example, that marine stratus below thin 166 cirrus are excluded). Furthermore, this one cloud must be (2) opaque (which means that low but 167 transparent clouds such as the ones reported in Leahy et al. [2012] are excluded), (3) spatially uniform 168 (i.e., detected at single-shot resolution within every laser pulse included in the 5 km averaging interval), 169 (4) assigned a high confidence score by the CALIOP cloud-aerosol discrimination (CAD) algorithm and 170 (5) identified as a high confidence water cloud by the CALIOP cloud phase identification 171 algorithm.When there is aerosol above OWCs, the lidar backscatter signal received from the underlying 172 water cloud is reduced in direct proportion to the two-way transmittance of the aerosol layer above. 173 Section B of the appendix provides additional information about the application of Eq. (2) and the 183 various steps needed to derive t DR AAC. We list the selection criteria used to identify the OWC dataset in 184 this study and describe the corrections required to obtain single-scattering estimates of IAB from 185 measurements that contain substantial contributions from multiple scattering (B1). We also describe the 186 technique used for distinguishing between CAC and AAC conditions (B2), and illustrate our derivation 187 of an empirical parameterization of IAB OWC SS,CAC as a global function of latitude and longitude (B3). 188 As reported in Table 2, the CALIOP DR method was used to study the African dust transport pathway 189 over the Tropical Atlantic  and the African smoke transport pathway over the South 190 East Atlantic Chand et al., 2008Chand et al., , 2009]. More recently, the CALIOP DR method was 191 also used by Deaconu et al. [2017] to assess POLDER AAC AOD values [Waquet et al., 2009[Waquet et al., , 2013b and Peers et al., 2015] over the globe. In this study, we extend the previous regional studies of [Liu et 193 [Fu and Liou, 1992] that is embedded within the LibRadtran 207 Radiative Transfer (RT) package [Emde et al., 2016]. Hereafter, our seasonally and spatially gridded (4º 208 x 5º) averaged shortwave (SW) (250 nm to 5600 nm) global TOA DAREcloudy results will be called 209 DAREOWC, as they pertain to a specific category of clouds (i.e., OWCs) defined according to the 210 CALIOP data selection criteria set forth in Table B2. We list the following input parameters to DISORT 211 in order to derive estimates of DAREOWC: 212 (1) Atmospheric profiles of pressure, temperature, air density, ozone, water vapor, CO2, and NO2 213 use standard US atmosphere profiles [Anderson et al., 1986]. 214 (2) Aerosol intensive radiative properties (i.e. properties that depend solely on aerosol species, 215 and are unrelated to the aerosol amount) are informed by seasonal maps (4º x 5º, daytime in 2007) 216 of combined MODIS-OMI-CALIOP (MOC) retrieved median spectral extinction coefficients, 217 single scattering albedos and asymmetry parameters at 30 different wavelengths. As an example, 218 Figure A1 in the appendix shows the seasonal maps of MOC SSA at 546.3 nm that were used in the 219 calculation of DAREOWC. These MOC retrievals, described in section A of the appendix, are at the 220 basis of a companion study [Redemann et al., 2018]. Let us note that we only use the shape of the 221 MOC extinction coefficient spectra and not its actual magnitude; the MOC spectral extinction 222 coefficient spectra is normalized to the seasonal 2008-2012 average value of either t DR AAC or t DR AAC 223 x fAAC within each grid cell. Our method assumes similar aerosol radiative properties above clouds 224 and in near-by clear-sky regions. 225 (3) Aerosol extensive radiative properties (i.e., properties that depend on the aerosol amount 226 present in the atmosphere) are informed by seasonal maps (4º x 5º, nighttime from 2008 to 2012) of 227 either CALIOP t DR AAC (see Eq. 2) or CALIOP t DR AAC x fAAC. We chose to use nighttime CALIOP 228 t DR AAC or t DR AAC x fAAC results in the estimation of DAREOWC because, at nighttime, the CALIOP 229 signal-to-noise-ratio (SNR) is not affected by ambient solar background and leads to a more 230 accurate measurement of the aerosol signal (compared to daytime). By doing this, we implicitly 231 chose a better accuracy in the aerosol extensive radiative properties over a temporal overlap 232 between aerosol extensive (nighttime) and intensive (daytime) radiative properties.

AAC Occurrence Frequencies 251
To provide the necessary context for interpreting our TOA radiative transfer calculations, we first 252 establish the observational AAC occurrence frequencies from which we will subsequently compute 253 estimates of DAREOWC. Figure 1 illustrates the annual gridded mean (5 years) global occurrence 254 frequencies of a) single layer clouds, b) opaque water clouds that are suitable for the DR method and c) 255 aerosol-above-clouds cases using the DR method. Figure 1d) Table B2), (b) opaque water clouds suitable for the DR method (C1-C5 of 262 Table B2; these clouds can be obstructed or unobstructed) and (c) AAC cases that show a positive 263 t DR AAC at 532 nm. (d) shows the difference between the number of AAC cases using the DR method 264 (i.e., number of cases with t DR AAC > 0) and the number of AAC cases using the standard Version 3 265 CALIOP product (i.e., number of cases with t STD AAC > 0); CALIOP AAC cases using the standard 266 algorithm are defined as 5 km-columns showing an uppermost layer classified as aerosols and a cloud 267 layer anywhere below that aerosol layer; the cloud itself does not have to satisfy any of the criteria of 268   Table B2) are detected in ~47% of all 5 km CALIOP 275 samples over the globe (see Figure 1(a)). In other words, at any one time, approximately half of the 276 globe is covered by uniform single layer clouds. As expected, the highest occurrence of those clouds is 277 in the high and low latitude bands and especially over the southern oceans. According to Figure 1( reduction from half-the-globe coverage is explained by the five criteria used to select OWCs for the 281 application of the DR method (i.e., C1-C5 of Table B2). The highest occurrence of OWCs can be found 282 offshore from the west coasts of North and South America, southwest Africa and Australia. In 283 particular, OWC cover ranges from 60 to 75 % over the region of SE Atlantic in August [Klein and 284 Hartmann, 1993]. Also, the southeastern Pacific region off the Peruvian and Chilean coasts is the 285 location of the largest and most persistent stratocumulus deck in the world [Klein and Hartmann, 1993]. 286 The percentage of AAC cases (i.e., AAC cases showing positive t DR AAC) at the basis of our study is 287 very small compared to the total number of 5 km CALIOP profiles per grid cell (i.e. mean of 5% on 288 Figure 1(c)). This is primarily due to a small number of low OWC used for the DR method over the 289 globe (when comparing Figure 1(a) and 1(b)). 290 we could be missing (in blue) AAC cases over most of the land surfaces and over the Arabian Sea, the 296 Tropical Atlantic and the SE Atlantic regions by using the DR method instead of the standard CALIOP 297 product. One reason for the lack of AAC cases offshore from the west coast of Africa in our dataset is 298 the filtering out of "unobstructed" but potentially aerosol-contaminated OWCs (see section B3 in the 299 appendix for more details). However, some regions such as the NE and SE Pacific exhibit up to 40% 300 more (in red) AAC cases when using the DR method. The SE Pacific region, especially offshore from 301 Chile, shows particularly tenuous aerosols, with attenuated backscatter values that typically fall below 302 the CALIOP detection limit and, hence, hampers the detection of AAC using the standard CALIOP 303 algorithm [Kacenelenbogen et al., 2014]. 304 In the rest of this study, the frequency of occurrence of AAC, fAAC, is defined as: 305 where NAAC is the number of AAC cases (i.e., cases showing a positive t DR AAC at 532nm) and NOWC is 307 fAAC of 58% to 61% with regional values that can reach more than 80% in some regions such as the SE 314 Atlantic, especially during the JJA season. The AAC occurrence frequencies in Fig

AAC Optical Depths, Extinction-to-Backscatter Ratios and South Atlantic Anomaly 327
Effects 328   Table 3 shows four different ways of computing global seasonal and annual averages of aerosol optical 343 depth above clouds: we use either t DR AAC or t DR AAC x fAAC (see Case I-II or III-IV) and then either (i) 344 exclude all cases of t DR AAC < 0 from the average (i.e., as in Case I and Case III), or (ii) set all cases of 345 t DR AAC < 0 to zero, and include these samples in the averages (i.e., as in Case II and Case IV). Let us 346 note that using t DR AAC x fAAC (instead of t DR AAC) acknowledges the fact that some OWCs present no 347 overlying aerosols. In this case, we assume that when the DR technique retrieves an invalid AAC 348 measurement, fAAC = 0 and there are no aerosols above the cloud. 349  Case III in Table 3). Note that if the white pixels were set equal to zero, the seasonal and annual global 364   Table 2) as 369 these studies use standard CALIOP Level 2 aerosol and cloud layer products for AAC observations,   season also shows a mean SAAC of ~50 ± 3 sr (in Fig. 5), which is consistent with the predominance of 405 Saharan dust (see Table B3). On the other hand, a primary aerosol source for the SEAt region is 406 biomass burning from South Africa (see references in Table 1 and 2 for AAC over SEAt). SEAt shows 407 higher mean SAAC values (i.e., above 60 sr in Fig. 5) in JJA, reflecting the presence of biomass burning 408 smoke aerosols (see Table B3). Let us note that SAAC values in our study are slightly lower than in [Liu 409 et al., 2015] (i.e., ~70 sr) over the SEAt region. This is most likely due to our approach to filtering the 410 OWC lidar ratios used in the DR method (see Fig. B3 in the appendix). 411          Figure 9a illustrates the mean regional, seasonal or annual estimates of SW TOA DAREOWC (W⸱m -2 ) in 503 each region of Table 6. CALIOP and (f) assumed underlying COD from MODIS in each region of Table 6. DAREOWC in (a) is 516 computed using the case IV of Table 5. 517 Table 7 reports the estimated seasonal or annual, regional range, mean and standard deviations of our 519 TOA DAREOWC dataset (i.e., values of Fig. 9a) 520 0.20 and 7.59 and within 0.07 and 5.72 W⸱m -2 ). The spread (i.e., standard deviation) on those mean 530 regional DAREOWC is of the same order of magnitude as the mean values themselves. For example, 531

AAC Optical Depths 329
although TAt shows an annual mean DAREOWC value of 0.41 W⸱m -2 , most points (i.e., about 68%, 532 assuming a normal distribution of DAREOWC) are within 0.41 ± 0.74 W⸱m -2 (see Table 7 We emphasize that the DAREOWC estimates in this study are not directly comparable to many previous 554 studies (see Table 1) because of different spatial domain, period, satellite sensors and associated 555 uncertainties. This will lead to the detection of different fractions of AAC above different types of 556 clouds and different AAC types over the globe. The calculations of DAREcloudy can also differ greatly 557 depending on different AAC aerosol radiative properties assumptions above clouds (especially 558 absorption) and different assumptions in aerosol and cloud vertical heights (see Table 1). 559 Apart from the major differences in methods and sensors, it seems reasonable to say that we are missing 560

Detecting and quantifying the true amount of AAC cases 583
Our study uses mainly CALIOP Level 1 measurements to detect aerosols above specific OWCs that 584 satisfy the criteria given in Table B2. We suggest that the number of CALIOP profiles that contain 585 aerosols over any type of cloud (instead of only OWCs in this study) should be informed by a 586 combination of different techniques applied to CALIOP observations (e.g., the standard products, the 587 DR and the CR technique). Airborne observations such as those from the ObseRvations of Aerosols  Table 2) and model simulations [Schulz et al., 2006]. propose that using a simple combination of MODIS TERRA and AQUA products would offer a 619 reasonable assessment of the daily averaged aerosol properties for an improved estimation of 24h-620 DAREnon-cloudy. 621

Considering the spatial and temporal variability of cloud and aerosol fields 622
We have used coarse resolution (i.e., 4ºx5º) seasonally gridded aerosol and cloud properties in our 623 DAREOWC calculations (see section 2.2). As a consequence, sub-grid scale variability (or heterogeneity) 624 of cloud and aerosol properties has not been considered. This approach is similar to assuming spatially 625 and temporally homogeneous cloud and aerosol fields in our DAREOWC results. subject to fresh local biomass emissions. In this type of environment, they observed a 19% variability of 642 the AOD over a 20 km length (comparable in scale to a ~0.1ºx0.1º area). They also found a 2% 643 variability in the AOD over the same length in a contrasting homogeneous environment that occurred 644 after a long-range aerosol transport event. As a consequence, similar to using a mean gridded 645 underlying COD and cloud Re, using mean gridded overlying aerosol radiative properties could very 646 well bias our DAREOWC results. As a preliminary investigation into the sources and magnitudes of these potential biases, we have used 648 TOA DAREnon-cloudy (see Eq. 1) estimates derived using well-collocated aerosol properties (hereafter 649 called "retrieve-then-average" or R-A) from a companion study (Redemann et al. [2018]; see section A 650 of the appendix) and compared those to DAREnon-cloudy estimates computed using seasonally gridded 651 mean aerosol properties at seasonally gridded mean vertical heights (hereafter called "average-then-652 retrieve" or A-R). Both DAREnon-cloudy results obtained with the two methods are compared over ocean 653 and at a resolution of 4ºx5º. 654 A majority (i.e., ~58%) of A-R DAREnon-cloudy results are within ±35% of the R-A DAREnon-cloudy 655 results. We find very few (i.e., ~1%) negative R-A DAREnon-cloudy values paired with positive A-R 656 DAREnon-cloudy values and very few large differences between both methods (i.e., less than 1% of the 657 differences are above ±10W m -2 ). However, we find a weak agreement between A-R and R-A   In the calculation of DAREOWC, we assume similar intensive aerosol properties above clouds and in have chosen for aggregating sub-grid aerosol and cloud spatial and temporal variability. We discuss 729 each of these in turn in the following paragraphs. 730 Two factors seem to be preventing the DR method from recording enough AAC cases in these regions: 731 the low cloud optical depths of underlying clouds and very few cases of "clear air" above clouds. The 732 DR method used in this study is restricted to aerosols above OWCs that satisfy a long list of criteria. 733 The AAC dataset in this study underestimates (i) the total number of CALIOP 5 km profiles that 734 contain AAC over all OWCs (i.e., not just suitable to the DR technique), (ii) the total number of 735 CALIOP 5 km profiles that contain AAC over any type of clouds over the globe and (iii) the true global 736 occurrence of AAC over any type of clouds. To the best of our knowledge, the true amount of AAC in 737  Table A1). The aerosol radiative properties resulting from this method are

785
The choice of OMI satellite algorithms (see Table A1) reflects their assessment of the 786 representativeness of subsampling OMI data along the CALIPSO track; i.e., they compared the 787 probability distribution (PDF) of the OMI retrievals along the CALIPSO track to the global PDF and 788 chose the data set that had the best match between global and along-track PDF for the over-ocean and 789 two over-land data sets, the latter being different in their use of MODIS dark target (DT) versus 790 For the OMAERUV data set, they choose the SSA product for the layer height indicated by the 793 collocated CALIOP backscatter profile. 794 Their aerosol models emulate those of the MODIS aerosol over-ocean algorithm [Remer et al., 2005]. 795 Like the MODIS algorithm, they define each model with a lognormal size distribution and wavelength-796 dependent refractive index. They then combine two of these models, weighted by their number 797 concentration, and compute optical properties for the bi-modal lognormal size distribution. Unlike the 798 MODIS algorithm, they allow combinations of two fine-mode or two coarse-mode models. They use 799 ten different aerosol models, which stem from some of the MODIS over-ocean models [Remer et al.,800 2005] but include more absorbing models, which was motivated by application of their methodology to 801 the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) 802 field campaign data, requiring more aerosol absorption than included in the current MODIS over-ocean 803 aerosol models. They use MOC spectral aerosol radiative properties to then calculate Direct Aerosol 804 Radiative Effects (i.e., DAREnon-cloudy, see Eq. 1) through a delta-four stream radiative transfer model 805 with fifteen spectral bands from 0.175 to 4.0 µm in SW and twelve longwave (LW) spectral bands 806 between 2850 and 0 cm -1 [Fu and Liou, 1992]. 807 In order to use these MOC parameters (retrieved in clear-skies) in our DAREOWC calculations, we need 808 to assume similar aerosol intensive properties in clear skies compared to above clouds and we need to 809 spatially and/ or temporally grid these MOC parameters. As discussed in section 2.2, we use seasonally 810 averaged MOC spectral SSA, aerosol asymmetry parameter, and extinction retrievals on 4ºx5º grids. The squares show different regions defined in Table 6. 816

817
The DAREOWC calculations in our study also require information about the underlying cloud optical 818 properties. As discussed in section 2.2, we use seasonally mean gridded COD from MODIS such as 819 illustrated in Figure A2.   Table 6. 826 827

Appendix B: Method for AAC detection, AAC AOD and SAAC computation 828
The depolarization ratio (DR) method [Hu et al., 2007b]  for both aerosol above cloud cases (X = AAC) and those cases with clear skies above (X = CAC). An 840 assumption of the DR method is that d OWC is negligibly affected by any aerosols that lie in the optical 841 path between the OWC and the lidar. 842 Table B1 provides a high-level overview of the procedure we use to compute aerosol optical depth 843 (t DR AAC) and aerosol extinction-to-backscatter ratio (SAAC) above OWCs over the globe. We chose to 844 concentrate on night-time CALIOP observations only, as they have substantially higher signal-to-noise 845 ratios (SNR) than the daytime measurements [Hunt et al., 2009]. 846 847 The first step (S1) is to identify OWCs that are suitable for the application of the DR method. The 852 acceptance criteria used to identify these clouds are described below in section B1 and listed in Table  853 B2. In the second step (S2), we use the overlying integrated attenuated backscatter (i.e., the 532 nm 854 attenuated backscatter coefficients integrated from TOA to the OWC cloud tops) to partition the OWC 855 into two classes: (i) "unobstructed" clouds, for which the magnitude of the overlying IAB suggests that 856 only aerosol-free clear skies lie above; and (ii) "obstructed" clouds for which we expect to be able to 857 retrieve positive estimates of τ DR AAC. Section B2 describes the objective method we have developed to 858 separate unobstructed clouds (for which we can compute IAB OWC SS,CAC) from obstructed clouds (for 859 which we calculate IAB OWC SS,AAC). 860 In step (S3), we construct global seasonal maps of median IAB OWC SS,CAC using 5 consecutive years 861 (2008-2012) of CALIOP nighttime data (see section B3). By doing this we can subsequently compute 862 estimates of t DR AAC without invoking assumptions about the lidar ratios of water clouds in clear skies 863 [Hu et al., 2007]. Throughout this study, we chose to compute global median values within each grid 864 cell (instead of mean values) to limit the impact of particularly high or low outliers on our statistics. 865 In step (S4), we compute estimates of t DR AAC for all obstructed OWC within each grid cell using Eq. (B4) 887 T 2 AAC(0,r) is the two-way aerosol two-way transmittance between the lidar (at range = 0) and range r. In 888 our application, rtop is the range bin immediately above the OWC top altitude, so that 889 solutions are obtained using an iterative method. Valid SAAC values must satisfy t DR AAC > 0 and SAAC > 897 0, and the iteration much converge to a solution for which the relative difference between successive 898 t DR AAC estimates is less than 0.01 (i.e. |(t DR AAC -t Fernald AAC)/t DR AAC| < 0.01). 899 Apart from the identification of specific OWCs in step (S1), the primary Level 2 CALIOP parameters 900 used to calculate t DR AAC (S2-S4 in Table B1) are (i) the integrated attenuated backscatter above cloud 901 top to detect "clear air" cases (i.e. "Overlying Integrated Attenuated Backscatter 532" in step (S2)), (ii) 902 the layer integrated attenuated backscatter of the OWC with clear air above (i.e. "Integrated Attenuated 903 Backscatter 532" in step (S3)) and (iii) the cloud multiple scattering factor, derived as a function of the 904 layer integrated volume depolarization ratio (i.e. the "Integrated Volume Depolarization Ratio" in S3 905 and S4). Concerning (b), we assume the influence of the SNR returned from the OWC is negligible as the OWCs 917 are strongly scattering features and our dataset is composed of nighttime data only. However, the 918 backscatter from tenuous and spatially diffuse aerosol layers with large extinction-to-backscatter ratios 919 can lie well beneath the CALIOP attenuated backscatter detection threshold. When such layers lie 920 above OWCs, the measured overlying integrated attenuated backscatter can fall within one standard 921 deviation of the expected 'purely molecular' value that is used to identify CAC (or "unobstructed") 922 OWC in our dataset (S2; see Sect. B2). Within the context of this study, these tenuous and spatially 923 diffuse aerosol layers can have appreciable AOD, and thus care must be taken to ensure that these sorts 924 of cases are not misclassified as CAC OWC. Section B3 discusses such cases, possibly found, for 925 example, over the region of SEAt. Successful application of the DR method (Eq. 2 or Eq. B1) requires a very specific type of underlying 929 cloud (step (S1) in Table B1). Table B2 lists the criteria we have applied to the CALIOP 5 km cloud 930 layer products for the selection of these specific OWCs over the globe. 931 932 Cloud detected at 5 km averaging resolution with CALIOP single shot cloud cleared fraction = 0 cloud is spatially uniform over a 5 km averaging interval C4 CALIOP opacity flag = 1; surface wind speed < 9 m/s cloud is opaque C5 CALIOP phase classification is high confidence water; δ OWC < 0.5; cloud top altitude < 3 km; cloud top temperature ≥ -10° C highly confident of cloud phase identification (water) We ensure that each cloud is the only cloud detected within the vertical column (C1) and is guaranteed 936 to be of high quality by imposing filters on various CALIOP quality assurance flags (C2). Imposing the 937 "single shot cloud cleared fraction = 0" in criterion (C3) assures that the clouds are uniformly detected 938 at single shot resolution throughout the full 5 km (15 shot) horizontal extent. As a result, we will 939 intentionally miss any broken clouds and any clouds that show a weaker scattering intensity within one 940 or more laser pulses with the 15 shot average. On the other hand, enforcing the single shot cloud 941 fraction = 0 criteria simultaneously ensures that all t DR AAC values in this study will lie below a certain 942 threshold: larger values would attenuate the signal to the point that single shot detection of underlying 943 clouds is no longer likely. Consequently, some highly attenuating biomass burning events (e.g., with 944 t DR AAC >2.5) can be excluded from the cases considered here. 945 At high surface wind speeds over oceans, the CALIOP V3 layer detection algorithm may fail to detect 946 surface backscatter signals underneath optically thick but not opaque layers. In such cases, CALIOP's 947 standard algorithm may misclassify the column as containing an opaque overlying cloud. To avoid such 948 scenarios, we exclude all the cases with high surface wind conditions (C4). Let us note that this 949 condition was applied on the entire dataset, disregarding the surface type (i.e. land or ocean), as our 950 OWC dataset resides mostly over ocean surfaces (see Figure 1b). 951 Criterion (C5) requires that the OWC be both low enough (cloud top below 3km) and warm enough 952 (cloud top temperature above -10ºC as in Zelinka et al. [2012]) to ensure that it is composed of liquid 953 water droplets. After applying all the criteria of Table B2, the median OWC top height of our dataset is 954 ~1.6 km. According to Hu et al. [2009], any feature showing a cloud layer integrated volume 955 depolarization ratio above 50% should correspond to an ice cloud with randomly oriented particles. 956 Criterion (C5) assures the deletion of such cases. 957 The averaged single-layer, high QA, uniform cloud (i.e. C1-C3 in Table B2) has a top altitude of ~8 958 km, a top temperature around -38º C and mean surface winds of ~6 m s -1 . Selecting only those clouds 959 with top temperatures above -10º C removes 30-40% of the observations. Subsequently filtering out 960 clouds with top heights above 3 km removes an additional 30% of the observations. Finally, filtering 961 out clouds with underlying winds above 9 m s -1 deletes another 20% of the observations. Among all 962 single-layer, high QA, uniform clouds (i.e. C1-C3 in Table B2), we find that ~45-50% are opaque 963 clouds (C4), and that ~11-12% satisfy all criteria (C1-C5) of Table B2. 964 965

B2. Select a subset of Opaque Water Clouds with clear air above 966
To distinguish between OWCs having clear skies above (i.e., unobstructed clouds, see S2 in Table B1) 967 and those having overlying aerosols, we examine the overlying integrated attenuated backscatter 968 reported in the CALIOP Level 2 cloud layer products. The total Integrated Attenuated Backscatter 969 (IAB) value above a cloud (i.e., IAB tot aboveCloud) can be written as follows: 970 (B6) 971 Here ba(r) and bm(r) are, respectively, the aerosol and the molecular backscatter coefficients (km -1 sr -1 ) 972 at range r (km), and T 2 a(0,r) and T 2 m(0,r) are the two-way transmittances between the lidar (at range r = 973 0) and range r due to, respectively, aerosols and molecules. 974 Figure B1 shows simulated profiles of the integrated attenuated backscatter above any given altitude, z, 975 (IAB mol above z) for a purely molecular atmosphere for both daytime (solid green curve) and nighttime 976 conditions (dashed green curve). These data were generated by the CALIPSO lidar simulator [Powell et