1 On the Relationship Between Environmental Parameters and Properties in 2 Stratocumulus Using Four Summers of Airborne Data Off the California Coast

3 4 1Department of Chemical and Environmental Engineering, University of Arizona, Tucson, AZ, 5 USA 6 2Department of Atmospheric Sciences, University of Arizona, Tucson, AZ, USA 7 NOAA 8 3Naval Postgraduate School, Monterey, CA, USA 9 4Department of Chemical Engineering, California Institute of Technology, Pasadena, CA, USA

10 *Corresponding author (phone: 520-626-5858, email: [email protected], address: PO 11 BOX 210011, Tucson, AZ 85721)

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12 Abstract 13 ….

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14 1. Introduction

15 Stratocumulus clouds have been studied extensively over numerous decades in part due 16 to both the challenge of explaining their nature and their importance to the planet’s energy 17 balance and other environmental issues (e.g., Wood et al., 2012). These clouds have a significant 18 impact on radiative forcing, physicochemical properties of aerosol particles, and biogeochemical 19 cycling of nutrients. Factors governing the microphysical and macrophysical properties of warm 20 clouds are a major source of uncertainty in climate models (e.g. Levin and Cotton, 2008; Stevens 21 and Feingold, 2009; Tao et al., 2012; Wood 2012; Boucher et al., 2013; Wang et al., 2013) 22 owing to a high degree of dynamical variability and the existence of multiple feedbacks. 23 The largest source of uncertainty in prediction is rooted in the effective 24 radiative forcing linked to aerosol-cloud interactions (IPCC, 2013). As a result, aggressive 25 research has focused on examining relationships between aerosol concentrations and cloud 26 properties such as the incidence and magnitude of (L’Ecuyer et al., 2009; Wang et 27 al., 2012), cloud microphysical parameters such as droplet effective radius, cloud drop number 28 concentration, and cloud optical depth (e.g., Feingold et al., 2003; McComiskey et al., 2009), 29 cloud fraction and macrophysical properties such as liquid water path (Albrecht et al., 1989; 30 Nakajima et al., 2001), albedo (Twomey et al., 1977a; Platnick and Twomey, 1994), and process 31 timescales such as converting cloud water to water (e.g., Sorooshian et al., 2013). Widely 32 accepted principles include that, at fixed LWP, cloud albedo increases with more aerosol due to 33 smaller but more numerous drops (Twomey et al., 1977a), and that collision-coalescence 34 between smaller drops is suppressed for more polluted clouds leading to suppressed precipitation 35 and changes in LWP (Albrecht et al., 1989). 36 A strategy employed to investigate the influence of aerosol on the aforementioned cloud 37 characteristics has been to examine correlations, quantification of physically-relevant metrics 38 (e.g., susceptibilities), and regression techniques to test and improve parameterizations employed 39 in models. A critical issue in these investigations has been the aerosol proxy used as there are 40 limitations associated with each type of measurement platform; for example, remote sensing 41 retrievals struggle to provide information strictly near cloud base while airborne measurements 42 struggle to provide broad spatiotemporal coverage and statistics. Furthermore, past studies have 43 mostly been focused on using only a proxy for aerosol concentration and did not probe deeper to 44 examine characteristics of the aerosol beyond just number concentration using in-situ 45 measurements. Characteristics that may have an impact, depending on environmental conditions, 46 include aerosol size distribution and chemical composition. 47 This study aims to use a multi-campaign dataset to examine interrelationships between 48 numerous cloud properties and aearosol physicochemical properties. A unique aspect of this 49 work is the extensive statistics collected over the course of four field campaigns in the exact 50 same region (coastal California coast) with nearly the same payload in the same months of the 51 year (July-August) when stratocumulus cloud cover is at a maximum. The structure of this paper 52 is as follows: (i) overview of campaigns and instrument datasets; examination of factors 53 governing (ii) cloud drop concentration, (iii) drop effective radiust, (iv) rate, and (v) 54 relationship between cloud thickness and LWP; and (vi) summary of results. 55 56 2. Experimental Methods 57 Airborne data are used from four field experiments based out of Marina, California using 58 the Center for Interdisciplinary Remotely-Piloted Aircraft Studies (CIRPAS) Twin Otter. The 59 first Marine Stratus/Stratocumulus Experiment (MASE-I; Lu et al., 2007) included 13 flights in

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60 July 2005, the second Marine Stratus/Stratocumulus Experiment (MASE-II; Lu et al., 2009) 61 included 16 research flights in July 2007, the Eastern Pacific Emitted Aerosol Cloud Experiment 62 (E-PEACE; Russell et al., 2013) included 30 flights between July and August in 2011, and the 63 Nucleation in California Experiment (NiCE) included 23 flights between July and August in 64 2013 (Coggon et al., 2014). 65 During these experiments, the Twin Otter conducted ~4-4.5 h flights at an airspeed of 66 ~50 m s-1 in the area encompassed by 34º N – 40º N and 121.5º W – 125º W with nearly the 67 same payload including the following: (i) particle number concentrations in the different size 68 ranges were observed with a condensation particle counter (CPC 3010; TSI Inc.; Dp > 10 nm), a 69 passive cavity aerosol spectrometer probe (PCASP; Dp ~ 0.1 – 2.6 μm), and a scanning mobility 70 particle sizer (SMPS; Dp ~ 15 nm — 800 nm) comprising a differential mobility analyzer (DMA 71 Model 3081, TSI Inc.) coupled to a CPC (Model 3010, TSI Inc.); (ii) droplet size distributions 72 between 0.4 μm and 1.6 mm were obtained with a cloud aerosol spectrometer (CAS), forward 73 scattering spectrometer probe (FSSP), and cloud imaging probe (CIP); (iii) sub-micrometer mass 74 concentrations of non-refractory aerosol constituents were obtained with an Aerodyne Aerosol 75 Mass Spectrometer (AMS; Drewnick et al., 2005); (iv) meteorological data (e.g., temperature, 76 humidity, winds, Gerber probe liquid water content (LWC; Gerber et al., 1994)). As presented in 77 numerous past studies (e.g., Prabhakar et al., 2014; Crosbie et al., 2016), the general flight 78 pattern used in the marine atmosphere is as follows: level legs below cloud base, immediate 79 above cloud base, at mid-cloud altitude, immediately below cloud top, immediately above cloud 80 top (called “wheels-in” leg), and a few hundred feet higher as part of a “free troposphere” leg. In 81 addition to the leg profiling, vertical soundings, either as a slant or spiral, were conducted before 82 and after each of these sets of leg patterns, from which column-integrated could be calculated. 83 Details of calculations of cloud parameters such as LWP, drop effective radius (re), cloud optical 84 depth (τ) and rain rate are summarized in past studies (e.g., Chen et al., 2012). Table 1 reports a 85 summary of nomenclature used to represent the aforementioned (and other) measurement 86 parameters. 87 Numerous calculations were made that required choices. Clear air is identified as having 88 liquid water content (LWC) values below 0.01 g m-3, and thus values exceeding this value were 89 used to identify cloud base and top heights. Inversion strength is calculated here as the difference 90 of potential temperature between the inversion-top and -base heights; inversion-base height is 91 defined as the altitude where temperature first reaches a minimum above the surface and the top 92 is defined as the height that the 5-s running mean of dθ/dz reaches a maximum. 93 94 3. Results and Discussion 95 In the subsequent discussion we examine interrelationships between microphysical and 96 macrophysical parameters relevant to aerosol particles and clouds, includng the following: (i) 97 cloud drop number concentration (Nd), (ii) cloud drop effective radius (re), (iii) drizzle rate (R), 98 and (iv) LWP. The number of data points used in the following analyses ranges between 135- 99 258, depending on the variables being used as some parameters may have been unavailable or 100 below detection limits. 101 102 3.1 Cloud Drop Number Concentration (Nd) 103 Two common ways field data are often used to examine the relationship between sub- 104 cloud aerosol concentraiton (Na) and cloud drop number concentration is with the ACI metric, 105 , and by power law regression fits, ∝ . ACIN is related to α, with values

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106 ranging from 0 to 1. A characteristic α value of ~0.7 has been proposed based on heuristics 107 (Twomey, 1977b). Reported α values from MASE I and MASE II were 0.563 and 0.594, 108 respectively (Lu et al., 2009). Factors that have been documented that increase the value of α 109 include increases in updraft velocity and adiabaticity, while reduced values are observed when 110 there is more active collision-coalescence and high Angstrom exponents (i.e., smaller aerosol) 111 (e.g., McComiskey et al., 2009). Leaitch et al. (1996) showed that Nd variance could be 112 explained better by Na and cloud water sulfate concentrations when data were separated into 113 categories of turbulence as quantified by the standard deviation of updraft velocity w΄ (σw). Lu et 114 al. (2007) also confirmed that inclusion of updraft velocity variabiity to Na values improved 115 predictions of Nd. Here we examine the ranking of the most important parameters in our dataset 116 to predict values of Nd. 117 Regression analysis was conducted to identify (i) the best single parameter to predict Nd, 118 (ii) the best two-parameter models, and (iii) the highest level of improvement in a two-parameter 119 model as compared to the individual single-parameter models (Table 2). Model rank is based on 120 values of the coefficient of determination (r2), which quantifies how much of the variabile in a 121 response variable is explained by the predictive variable(s). A P value is reported for each 122 regression to quantify the significance level of an individual model, with values < 0.05 123 considered here to be significant; values above 0.05 mean that the null hypothesis cannot be 124 rejected that the model predicts the response variable better than the intercept-only model. 125 126 3.1.1 Single Parameter Models 127 Within the three strongest single parameter models were the predictive variables drop 128 effective radius (re) and rain rate (R), but since these parameters are considered to be a 129 consequence of Nd values, more focus is placed on models with parameters that are thought to be 130 precursor factors in altering Nd. Among the other single parameter models, the strongest ones 131 included an aerosol number concentration proxy, followed by above-cloud thermodynamic 132 variables, and sub-cloud σw. More specifically, the second best model was for sub-cloud Na, as 133 measured by the PCASP (Dp > 100 nm), which is a better proxy measurement for CCN 134 concentration as compared to CPC (Dp > 10 nm; rank = 5) measurements since the activation 135 diameter of particles in the region is much closer to 100 nm than 10 nm (e.g., Wonaschuetz et al., 136 2013). The power law exponent α, when using Na from PCASP and CPC, is 0.54 and 0.25, 137 respectively, with the lower value from the CPC being due to the considerably large amount of 138 number concentration between 10—100 nm that may not be at CCN-relevant sizes as compared 2 2 139 to particles above 100 nm. Values of r dropped significantly after the Na model (r = 0.47), with 2 140 other notable models being for σw (r = 0.12) and thermodynamic variables above cloud top 141 (inversion strength and temperature: r2 = 0.17). 142 In terms of aerosol mass and composition, the r2 of models considering mass 143 concentration of total non-refractory sub-micrometer constituents, inorganics, and sulfate was 144 similar (0.11), whereas that for organics was lower (0.06). Models containing size distribution 2 145 parameters (D0.5, GSD) were even weaker (r = 0.01-0.02), followed by surface-level GCCN and 2 146 mass fractions of sulfate and either organics or inorganics (r ≤ 0.01); only D0.5 exhibited a P 147 value less than 0.05 of these last six models. 148 149 3.1.2 Double Parameter Models 150 The 55 highest ranked double parameter models included re as one of the two predictive 151 variables along with a suite of other parameters such as LWP and sub-cloud Na which exhibited

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152 the two highest r2 values (0.88 and 0.84, respectively). The first two models without re include 2 153 Na and either R or Rcb as predictors (r = 0.57-0.64), with the latter two exhibiting a negative 154 exponent due to the coincidence of more rain and with enhanced collision-coalescence to 2 155 decrease Nd in cloud. The next notable model includes Na and σw (r = 0.54), with the latter 156 having a positive exponent due to higher supersaturations achieved and thus greater ease of 157 particle activation into drops. In terms of models with other aerosol parameters in addition to Na 158 were three with mass fractions for sulfate (r2 = 0.52), organics (r2 = 0.49), and inorganics (r2 = 159 0.49). Models exhibiting the greatest level of r2 improvement due to a second variable added 160 included those with either Na or CN and either R or Rcb. Therefore, although mass fractions 161 ranked lower than mass concentrations, GSD, and D0.5 in the single parameter models, they 162 strengthened two parameter models the most in terms of an aerosol parameter to add to Na or 163 CN; however, the level of r2 improvement is weak when adding any information about 164 composition to aerosol number concentration (≤ 0.02) with the exception of adding MFSO4 to Na 165 (improvement of 0.09). 166 167 3.1.3 Binning Analysis 168 It is of interest to look more closely at how ACI depends on potentially influential 169 factors. Figure 2 shows how ACI is relatively stable as a function of D0.5 until reaching the very 170 largest bin, suggestive of how the largest aerosol probed exhibited increased likelihood to 171 activate into drops. The reduction of ACI as a function of R is further supportive of previous 172 reports of how collision-coalescence in precipitating clouds can obfuscate the desired 173 relationship that ACI serves to probe. ACI increases as a function of σw due to higher 174 supersaturations expected under such conditions. 175 Previous modeling work has shown that in regimes with high ratios of updraft velocity 176 (w) to aerosol concentration, that Nd is proportional to aerosol concentration and practically 177 independent of w (Reutter et al., 2009); conversely, they showed that low ratios are characterized 178 by Nd being directly proportional to w and independent of aerosol concentration. Figure 3 179 attempts to validate such results with observations by examining the relationship between Nd 180 and CN in bins of σw:CN. In agreement with Reutter et al. (2009), our data shows that low ratios 181 coincide with Nd being positively related to σw and with a lack of relationship with CN. At high 182 ratios, Nd is more strongly related to CN, and, while still positively related, it is more weakly 183 related now to σw. 184 185 3.2 Cloud Drop Effective Radius 186 Analagous to Nd, relationships between aerosol and re have been studied extensively 187 using the ACI metric, (at fixed cloud macrophysical conditions) and power law 188 regression fits such as ∝ . Since LWP is often the macrophysical cloud property 189 held fixed when quantifying ACI, the value of ACIre is directly related to β2 in the power law. 190 With basic assumptions of a homogeneous cloud with constamt Nd and LWC, β1 = 0.33 and β2 = 191 α/3 (Feingold et al., 2003). 192 A wide range of ACI values has been reported in the literature (e.g., Kim et al., 2003; 193 Garrett et al., 2004; Tang et al., 2011; Zhao et al., 2012), with higher values usually associated 194 with in-situ and ground-based measurements as compared to satellite remote sensing 195 observations (McComiskey and Feingold, 2008); that study showed that a wide range of 196 radiative forcing estimates (from -3 to -10 W m-2) can result simply from a difference in ACI of 197 0.05.

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198 199 3.2.1 Single Parameter Models 2 2 200 When excluding models with R (r = 0.63) and Rcb (r = 0.41), which are due to them 201 being a consequence of high re values, regressions relying on either drop or aerosol number 2 202 concentration were the highest ranked (Table 3). Nd was the best predictive variable (r = 0.82), 2 203 followed by, in decreasing r value, sub-cloud Na, surface level Na, above-cloud Na, and above- 204 cloud CN from the CPC (r2 = 0.15 – 0.28). Of note is that inverstion strength is negatively th 2 205 related to re in the 10 ranked model (r = -0.12), consistent with its positive associated with Nd 206 in Table 2. th 207 The 13 ranked model included σw, with a negative dependence owing likely to lower 208 supersaturations at lower values of σw that limit drop activation to larger particles, thereby 209 suppressing Nd. While a number of mass concentration variables are negatively related to re, 210 owing to their positive association with aerosol concentration, GCCN concentration is instead 211 positively associated with re in the 15th ranked model; this could be owing to enhanced collision 212 coalescence leading to larger re values. 213 214 3.1.2 Double Parameter Models 2 215 The top ranked models include Nd and either R, Rcb, LWP, depth, or adiabaticity (r = 216 0.83 – 0.93); Nd always exhibits a negative exponent while the second variable is positive. 217 Models exhibiting the strongest improvement in r2 with the inclusion of a second variable 218 included those with Na and either depth, R, Rcb, and q. Detailed aerosol physicochemical 219 properties (D0.5, GSD, composition) only appeared in poorly ranked models as their effects were 220 contained within Nd and also could have been much weaker than the impact of just using aerosol 221 concentration. 222 223 3.2.3 Binning Analysis 224 225 226 3.3 Drizze Rate 227 Of relevance to warm clouds is the power law representing autoconversion, R 228 LWP N (e.g., Khairoutdinov and Kogan, 2000), where LWP is liquid water path and Nd is 229 cloud drop number concentration. Some studies have used multivariate linear regression fits to 230 the logarithms of values for R, LWP, and Nd to test and suggest methods of improving this 231 parameterization for specific cloud types. Jiang et al. (2013) did such an exercise and concluded 232 that if another term is added for cloud lifetime that R could be more reliably predicted for warm 233 trade cumulus clouds. Other studies have focused exclusively on specific exponents in the power 234 law for R. For example, to study the nature of the β parameter, the precipitation susceptibility 235 metric (So = ) was introduced, which relates a change in drop number 236 concentration Nd (or related proxies) to a change in precipitation rate (R) at fixed cloud 237 macrophysical conditions (e.g., LWP or cloud thickness) (Feingold and Siebert, 2009). 238 Numerous studies have examined how So depends on a macrophysical property assumed 239 to include meteorological influences on the cloud, including LWP (e.g., Lu et al., 2009; Wood et 240 al., 2009; Sorooshian et al., 2009, 2010; Jiang et al., 2010; Bangert et al., 2011; Duong et al., 241 2011; Gettelman et al., 2013; Mann et al., 2014) and cloud thickness (Terai et al., 2012). Studies 242 differ in reported absolute values of So and their behavior as a function of the chosen

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243 macrophysical proxy. For example, some studies report that So typically increases up to a 244 specific LWP at which point it drops in value reflecting a switch from a dominant 245 autoconversion process to an accretion process. The other subset of studies, focused mainly on 246 stratocumulus clouds, report a general reduction in So as a function of LWP or cloud thickness. 247 Differences in these studies include (but are not limited to) differences in the following: (i) cloud 248 type (Lebo and Feingold, 2014), (ii) choices of how to calculate parameters included in 249 quantifying So (Duong et al., 2011), (iii) minimum threshold value for rain rate (Duong et al., 250 2011), (iv) lower tropospheric static stability (Sorooshian et al., 2009), (v) and ‘cloud contact 251 time’, defined as the time an air parcel spends in cloud (Feingold et al., 2013). The choice of 252 whether to include non-precipitating clouds in the analysis also can lead to conflicting results 253 between studies, and thus, the use of “SI” (henceforth referrred to as So) introduced by Terai et al. 254 (2012) most closely matches So examined in this study for precipitating clouds. Terai et al. 255 (2015) concluded in their recent investigation of So across different regions that Nd and LWP are 256 insufficient in terms of governing factors and that other controls exist that need to be identified to 257 connect regional and global estimates. Interestingly, they observed negative values of So for thin 258 and polluted clouds, and speculated that other factors can help explain such unintuitive results 259 including turbulence, giant cloud condensation nuclei (GCCN), and satellite retrieval artifacts. 260 These other factors and others require warrant attention in a focused study examining one cloud 261 regime with a decent amount of statistics. 262 263 3.3.1 Single Parameter Models 264 The highest ranked models to predict R, aside from the related Rcb parameter, include re 265 (r2 = 0.63), Nd (r2 = 0.34), depth (r2 = 0.27), and LWP(r2 = 0.16) (Table 4). In terms of aerosol 266 parameters, interestingly the best model was for GCCN (r2 = 0.13) with a positive exponent 267 indicative of enhancement of collision-coalesence, which is consistent with its positive 268 relationship with re in Table 4. The next strongest models included various mass concentration 269 variables (total, sulfate, organic, inorganic: r2 = 0.08 – 0.9) that were negatively related owing to 270 their covariance with aerosol number concentration. 271 272 3.3.2 Double Parameter Models 273 The highest ranked model that excludes the obvious variable Rcb, includes re and either 2 2 2 2 274 LWP (r = 0.77), Na (r = 0.75), depth (r = 0.74), and Nd (r = 0.73). The commonly employed nd 275 autoconversion parameterization relying on Nd and LWP registered as the 82 best model but 276 with a similarly high r2 value of 0.63 and the highest improvement of any model when adding a 277 second variable. 278 279 3.4 LWP 280 Liquid water path is signifcant as not only a key macrophysical cloud property driving 281 reflectivity and precipitation, but also as a key variable held fixed in studies of how aerosol 282 perturbations impact cloud microphysical properties. 283 284 Owing to the importance of holding macrophysical cloud properties constant when 285 examining relationships between aerosol properties and cloud properties (i.e., to hold 286 meteorological factors constant), we examine relationships between cloud thickness and LWP as 287 these two are the most commonly used macrophysical property that is held constant. An

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288 adiabatic assumption is often employed to relate these two parameters (e.g., Albrecht et al., 289 1990; Austin et al., 1995; Wood and Taylor, 2001; Zhou et al., 2006) 290 291 ∝ (1) 292 where α is precentage of adiabaticity and A is the adiabatic rate of change of height with LWC. 293 While adiabatic (or near-adiabatic) liquid water content profiles are well documented (e.g., 294 Slingo et al., 1982; Gerber et al., 1994), (i) sub-adiabatic and (ii) super-adiabatic profiles have 295 also been reported due to (i) entrainment or drizzle (Wood and Taylor, 2001) and (ii) decoupled 296 boundary layers where detraining cumulus plumes enhance stratocumulus layers (Miller et al., 297 1998), respectively. Others have noted different relationships between LWP and H such as 298 ∝ based on CloudSat LWP and CALIPSO thickness data (Brunke et al., 2010). Better 299 understanding the nature of this relationship will benefit model parameterizations that are used 300 for radiation calculations and for the purposes of intercomparisons of aerosol-cloud interaction 301 studies that use both LWP and H as the macrophysical cloud property held fixed to account for 302 meteorological influences on clouds. 303 304 3.4.1 Single Parameter Models 305 As expected, depth is the strongest predictive variable for LWP (r2 = 0.69). The next best 306 models exhibited a steep drop off in r2 values: cloud top height (0.19), R (0.16). 307 308 3.4.2 Double Parameter Models 309 The strongest two models with two parameters contained depth and eiehter Nd or GCCN 310 (r2 = 0.78). The model including depth and adiabaticity was the 35th best model (r2 = 0.71). Aside 311 from the obvious improvement in r2 expected when coupling cloud base and top height (0.42), 312 the next few models exhibiting the highest r2 improvement included re-Nd, R-Nd, R-re, and R- 313 Htop (0.12 – 0.38). 314 315 316 4. Conclusions 317 This study … 318

319 320 Acknowledgements 321 All data and results are available from the corresponding author ([email protected]). 322 This work was funded by NASA grant NNX14AM02G and Office of Naval Research grants 323 N00014‐10‐1‐0811, N00014-11-1-0783, N00014-10-1-0200, and N00014-04-1-0118. 324 325 References 326 Albrecht, B. (1989), Aerosols, cloud microphysics, and fractional cloudiness, Science, 245, 327 1227–1230, doi:10.1126/science.245.4923.1227. 328 329 Albrecht, B. A., C. W. Fairall, D. W. Thomson, A. B. White, J. B. Snider, and W. H. Schubert 330 (1990), Surface-Based Remote-Sensing of the Observed and the Adiabatic Liquid Water-Content 331 of Stratocumulus Clouds, Geophys Res Lett, 17(1), 89-92. 332

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465 Terai, C. R., R. Wood, D. C. Leon, and P. Zuidema (2012), Does precipitation susceptibility vary 466 with increasing cloud thickness in marine stratocumulus?, Atmos. Chem. Phys., 12(10), 4567- 467 4583. 468 469 Terai, C. R., R. Wood, and T. L. Kubar (2015), Satellite estimates of precipitation susceptibility 470 in low-level, marine stratocumulus, J. Geophys. Res. 471 472 Twomey, S. (1977a), Influence of Pollution on Shortwave Albedo of Clouds, J Atmos Sci, 34(7), 473 1149-1152. 474 475 Twomey, S., Atmospheric Aerosols, Elsevier Sci, New York, 1977b. van de Hulst, H. C., Light 476 Scattering by Small Particles, Dover, Mineola, 477 New York, 1981. 478 479 Wang, M. H., et al. (2012), Constraining cloud lifetime effects of aerosols using A-Train satellite 480 observations, Geophys Res Lett, 39. 481 482 Wonaschutz, A., et al. (2013), Hygroscopic properties of smoke-generated organic aerosol 483 particles emitted in the marine atmosphere, Atmos. Chem. Phys., 13(19), 9819-9835. 484 485 Wood, R. (2012), Stratocumulus Clouds, Mon. Rev., 140(8), 2373-2423. 486 487 Wood, R., and J. P. Taylor (2001), Liquid water path variability in unbroken marine 488 stratocumulus cloud, Q J Roy Meteor Soc, 127(578), 2635-2662. 489 490 Wood, R., T. L. Kubar, and D. L. Hartmann (2009), Understanding the importance of 491 microphysics and macrophysics for warm rain in marine low clouds. Part II: Heuristic models of 492 rain formation, J. Atmos. Sci., 66(10), 2973-2990. 493 494 Zhao, C. F., Klein, S. A., Xie, S. C., Liu, X. H., Boyle, J. S., Zhang, Y. Y. (2012). Aerosol first 495 indirect effects on non-precipitating low-level liquid cloud properties as simulated by CAM5 at 496 ARM sites, Geophys. Res. Lett., 39, L08806, doi:10.1029/2012GL051213.

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500

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501 Table 1. Summary of variable names. 502 Acronym Description

Aerosol Size Distribution Na Sub-cloud PCASP concentration (> 100 nm) CN Sub-cloud CPC concentration (> 10 nm)

D0.5 Geometric median diameter of size distribution (DMA) GSD Geometric standard deviation of size distribution (DMA) GCCN Near surface GCCN concentration above 5 µm (CAS)

Aerosol Composition (AMS) SO4 Sulfate

NO3 Nitrate

NH4 Ammonium

Inorg Inorganic (SO4+ NH4 + NO3) Org Organic Total Inorganic + Organic MF Mass fraction Mass Mass concentration Cloud Adia Adiabaticity LWP Liquid water path

re Drop effective radius

Hbase Cloud base height

Htop Cloud top height R Columnar rain rate

Rcb Cloud base rain rate

Nd Columnar cloud drop concentration Met/Thermo T Temperature q Specific humidity Wind Wind speed Depth Cloud thickness RH Relative humidity SST Skin surface temperature InvStrength Inversion strength InvDepth Inversion layer depth

σw Standard deviation of sub-cloud vertical wind velocity Location SF Near surface measurement 503 AT Above cloud top measurement

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504 Table 2. Summary of 1- and 2-parameter regression models to predict Nd. In terms of model 505 rankings, based on r2 values, there were XX and YY total models for the single- and double- 506 parameter models, respectively. 507 Regression Rank αβr2 P value r2 improvement n α Nd~re 1 -2.41 0.78 8.36E-86 258 α Nd~Na 2 0.54 0.47 4.75E-29 202 α Nd~R 3 -0.39 0.32 1.11E-21 242 α Nd~Na,SF 4 0.44 0.30 8.20E-21 246 α Nd~CN 5 0.25 0.19 3.84E-11 209 α Nd~NAT 6 0.22 0.18 6.55E-10 198 α Nd~Rcb 7 -0.25 0.17 7.60E-10 201 α Nd~TAT 8 1.18 0.17 6.02E-11 230 α Nd~InvStrength 9 0.38 0.17 1.90E-11 242 α Nd~CNSF 10 0.19 0.14 1.39E-09 242 α Nd~RHSF 11 -1.54 0.13 3.91E-09 256 α Nd~σw 12 0.32 0.12 7.59E-08 232 α Nd~MassTotal 13 0.23 0.11 1.92E-05 157 α Nd~MassInorg 14 0.23 0.11 2.00E-05 157 α Nd~MassSO4 15 0.18 0.11 2.91E-05 157 α Nd~CNAT 16 0.21 0.10 2.97E-06 205 α Nd~RHAT 17 -0.31 0.10 1.16E-05 181 α Nd~MassOrg 24 0.15 0.06 3.09E-03 153 α Nd~D0.5 33 0.25 0.02 3.10E-02 204 α Nd~GSD 38 0.27 0.01 8.22E-02 204 α Nd~GCCNSF 41 -0.04 0.01 2.02E-01 157 α Nd~MFSO4 43 0.08 0.01 2.48E-01 154 α Nd~MFInorg 50 0.08 0.00 4.93E-01 153 α Nd~MFOrg 52 -0.03 0.00 7.92E-01 153 α β Nd~LWP re 1 0.25 -2.71 0.88 2.62E-101 0.09 221 α β Nd~Na re 2 0.27 -1.81 0.84 2.32E-79 0.09 200 α β Nd~Na R 56 0.46 -0.28 0.64 2.98E-41 0.18 187 α β Nd~Na Rcb 57 0.54 -0.20 0.57 5.54E-29 0.13 157 α β Nd~Na σw 58 0.49 0.25 0.54 1.38E-32 0.08 191 α β Nd~Na MFSO4 61 0.65 0.23 0.52 1.19E-22 0.09 136 α β Nd~Na MFOrg 66 0.68 -0.20 0.49 2.84E-20 0.02 135 α β Nd~Na MFInorg 68 0.67 0.20 0.49 3.79E-20 0.02 135 α β Nd~CN R 92 0.24 -0.35 0.46 2.45E-26 0.18 195 α β Nd~InvStrength InvDepth 94 0.65 -0.37 0.45 5.91E-32 0.27 241 α β Nd~CN Rcb 169 0.24 -0.23 0.33 1.49E-14 0.17 161 α β Nd~CN D0.5 221 0.32 0.52 0.26 1.76E-12 0.08 179 α β Nd~CN σw 243 0.20 0.21 0.25 1.15E-12 0.05 198 α β Nd~CN MFSO4 281 0.35 0.15 0.22 1.55E-08 0.05 143 α β Nd~CN GSD 303 0.26 0.34 0.21 1.12E-09 0.03 179 α β Nd~CN MFOrg 408 0.31 -0.08 0.18 9.68E-07 0.00 142 α β 508 Nd~CN MFInorg 415 0.30 0.07 0.18 1.05E-06 0.00 142

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509 Table 3. Summary of 1- and 2-parameter regression models to predict re. In terms of model 510 rankings, based on r2 values, there were XX and YY total models for the single- and double- 511 parameter models, respectively. 512 Regression Rank αβr2 P value r2 improvement n α re~Nd 1 -0.32 0.82 7.08E-77 205 α re~R 2 0.20 0.63 1.56E-43 193 α re~Rcb 3 0.14 0.41 7.20E-19 153 α re~Na 4 -0.15 0.28 3.99E-12 150 α re~Na,SF 5 -0.13 0.22 1.01E-11 192 α re~Na,AT 6 -0.09 0.19 3.17E-08 146 α re~CNAT 7 -0.10 0.15 7.62E-07 153 α re~RHSF 8 0.56 0.14 3.51E-08 201 α re~MassTotal 9 -0.10 0.14 3.68E-05 114 α re~InvStrength 10 -0.12 0.14 1.61E-07 190 α re~MassInorg 11 -0.10 0.13 1.06E-04 114 α re~MassOrg 12 -0.08 0.12 1.44E-04 113 α re~σw 13 -0.12 0.12 2.45E-06 179 α re~MassNO3 14 -0.08 0.10 5.86E-04 114 α re~GCCN 15 0.05 0.10 4.78E-04 120 α β re~Nd R 1 -0.24 0.10 0.93 3.78E-108 0.11 193 α β re~Nd LWP 2 -0.34 0.08 0.90 6.96E-84 0.06 169 α β re~Nd Rcb 3 -0.28 0.06 0.90 2.25E-74 0.06 153 α β re~Nd Depth 4 -0.32 0.13 0.88 7.35E-93 0.06 204 α β re~Nd Adiabaticity 7 -0.33 0.05 0.83 3.72E-76 0.01 197 α β re~Na R 29 -0.10 0.18 0.81 1.27E-50 0.14 141 α β re~LWP R 58 -0.09 0.23 0.73 7.72E-45 0.06 160 α β re~Na Rcb 90 -0.14 0.13 0.67 6.17E-27 0.21 112 α β re~Na Depth 120 0.25 -0.16 0.50 8.10E-23 0.22 150 α β re~InvStrength InvDepth 170 -0.2 0.1 0.34 1.98E-17 0.18 189 α β 513 re~Na q 178 -0.2 0.86 0.32 2.19E-15 0.21 175 514 515

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516 517 Table 4. Summary of 1- and 2-parameter regression models to predict R. In terms of model 518 rankings, based on r2 values, there were XX and YY total models for the single- and double- 519 parameter models, respectively. 520 Regression Rank αβr2 P value r2 improvement n α R~re 1 3.20 0.63 1.56E-43 193 α R~Rcb 2 0.68 0.57 3.86E-30 155 α R~Nd 3 -0.83 0.34 6.27E-19 195 R~Depthα 4 1.17 0.27 3.33E-15 198 R~LWPα 5 0.58 0.16 1.12E-07 164 R~GCCNα 6 0.28 0.13 5.18E-05 118 α R~MassTotal 7 -0.37 0.09 2.06E-03 108 α R~MassSO4 8 -0.26 0.08 2.71E-03 108 α R~D0.5 9 -0.71 0.08 4.06E-04 155 α R~MassOrg 10 -0.27 0.08 3.44E-03 107 α R~MassInorg 11 -0.36 0.08 3.69E-03 108 α β R~re Rcb 1 2.18 0.37 0.77 4.31E-48 0.10 151 α β R~re LWP 2 3.13 0.45 0.77 7.77E-51 0.11 160 α β R~re Na 3 4.16 0.38 0.75 1.90E-42 0.08 141 α β R~Depth Rcb 4 1.03 0.55 0.74 3.78E-45 0.17 155 α β R~re Depth 5 2.87 0.72 0.74 6.83E-56 0.10 193 α β R~re Nd 6 5.89 1.05 0.73 1.96E-55 0.10 193 α β R~LWP Nd 82 0.70 -0.98 0.63 4.26E-35 0.25 161 α β 95 1.09 -0.82 0.59 1.22E-37 0.25 195 521 R~Depth Nd 522

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523 Table 4. Summary of 1- and 2-parameter regression models to predict LWP. In terms of model 524 rankings, based on r2 values, there were XX and YY total models for the single- and double- 525 parameter models, respectively. 526 527 Regression Rank αβr2 P value r2 improvement n LWP~Depthα 1 1.29 0.69 6.17E-48 183 α LWP~Htop 2 0.84 0.19 4.94E-10 183 LWP~Rα 3 0.28 0.16 1.12E-07 164 α LWP~WindAT 4 -0.29 0.06 2.28E-03 157 LWP~Adiabaticity_Hα 22 0.17 0.01 1.45E-01 173 α LWP~Hbase 53 0.02 0.00 8.04E-01 183 α β LWP~Depth Nd 1 1.50 0.24 0.78 3.83E-56 0.05 170 LWP~Depthα GCCNβ 2 1.50 0.02 0.78 7.04E-36 0.00 109 LWP~Depthα Adiabaticityβ 35 1.31 0.23 0.71 2.00E-46 0.02 173 α β LWP~Htop Hbase 54 2.75 -1.38 0.61 1.15E-37 0.42 183 α β LWP~R Nd 55 0.58 0.65 0.42 3.43E-19 0.25 161 α β LWP~re Nd 56 4.64 1.63 0.40 3.35E-19 0.38 169 α β LWP~R Htop 58 0.24 0.78 0.34 2.20E-15 0.12 164 α β 60 0.70 -1.96 0.32 5.35E-14 0.15 160 528 LWP~R re 529

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530 531 Figure 1. Dependence of ACI (using sub-cloud CN from CPC as aerosol proxy) on geometric 532 median diameter, rain rate, and sub-cloud vertical wind standard deviation. 533

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534 535 Figure 2. Relationship between Nd and sub-cloud CPC aerosol concentration (CN) in bins of 536 σw/CN. The inset boxes show results of two-parameter regression models for each bin.

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537 538 539 Figure Y. So-LWP relationship based on airborne data frrom four fielld campaigns. 540 541 542 543 544

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