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ISSN : 1225-6692(Print)
ISSN : 2287-4518(Online)
Journal of the Korean earth science society Vol.43 No.4 pp.498-510
DOI : https://doi.org/10.5467/JKESS.2022.43.4.498

# Observational Evidence of Giant Cloud Condensation Nucleus Effects on the Precipitation Sensitivity in Marine Stratocumulus Clouds

Eunsil Jung*
Department of Advanced Science and Technology Convergence, Kyungpook National University, Sangju 37224, Korea
*Corresponding author: eunsil.jung@knu.ac.kr Tel: +82-54-530-1445
July 21, 2022 August 22, 2022

## Abstract

Cloud-aerosol interactions are one of the paramount but least understood forcing factors in climate systems. Generally, an increase in the concentration of aerosols increases the concentration of cloud droplet numbers, implying that clouds tend to persist for longer than usual, suppressing precipitation in the warm boundary layer. The cloud lifetime effect has been the center of discussion in the scientific community, partly because of the lack of cloud life cycle observations and partly because of cloud problems. In this study, the precipitation susceptibility (So) matrix was employed to estimate the aerosols' effect on precipitation, while the non-aerosol effect is minimized. The So was calculated for the typical coupled, well-mixed maritime stratocumulus decks and giant cloud condensation nucleus (GCCN) seeded clouds. The GCCN— artificially introduced to the marine stratocumulus cloud decks—is shown to initiate precipitation and reduces So to approximately zero, demonstrating the cloud lifetime hypothesis. The results suggest that the response of precipitation to changes in GCCN must be considered for accurate prediction of aerosol-cloud-precipitation interaction by model studies

## Introduction

The warm boundary layer clouds under high aerosol concentrations tend to live longer as aerosols serve as cloud condensation nuclei and produce numerous small cloud droplets, increasing the cloud amount and suppressing the precipitation (cloud lifetime effect). The cloud lifetime effect (Albrecht, 1989) has been the center of discussion since it was first proposed three decades ago, partly due to the lack of observations of the cloud life cycle and partly due to the so-called cloud problem (Stevens and Feingold, 2009). Previous studies have shown inconsistent results in aerosol effects on precipitation—precipitation either decreases or increases as aerosol increases (Kaufman et al., 2005;Norris, 2001;Jiang et al., 2006;Xue and Feingold, 2006).

The response of precipitation to aerosol loading differs between small- and large-sized aerosol particles. The increase of small-sized aerosols (such as sulfates) suppresses precipitation due to the inefficient collision and coalescence process among small cloud droplets. By contrast, the increase of large-sized aerosols (e.g., sea sprays and soluble dust particles) can accelerate the collision and coalescence process. A fast-falling larger droplet catches slow-falling smaller droplets on the path of its fall through the cloud, and the larger droplet grows even larger and increases precipitation (Woodcock, 1952, 1953;Johnson, 1976;Feingold et al., 1999;Lasher-Trapp et al., 2001;L’Ecuyer et al., 2009;Jung et al., 2015). Moreover, factors other than aerosol loading can affect and modulate precipitation production; thus, developing the causality relationship between changes in aerosol loading and precipitation is challenging.

There are two strategies to estimate aerosols' effects on precipitation while minimizing the non-aerosol effects. One is to examine precipitation changes with aerosol loading under identical (or similar at least) meteorological conditions. The other is to use the precipitation susceptibility matrix, which will be discussed later in detail in the method section.

In principle, well-developed, uniform marine stratocumulus (Sc) cloud decks present laboratory-like conditions in which the cloud properties change little over time. Therefore, the cloud field can be used to evaluate the effect of changes of aerosols on cloud properties. Indeed, Jung et al. (2015) demonstrated the impacts of giant cloud condensation nuclei (GCCN) on initiating warm precipitation in the unbroken, homogeneous Sc decks in the Northeast Pacific (NEP). They directly introduced GCCN into the Sc cloud and compared the properties of seeded cloud regions with the controlled background cloud conditions during the Eastern-Pacific Emitted Aerosol Cloud Experiment (EPEACE, Russell et al., 2013). The added GCCN enhanced precipitation four-folds. However, they did not show the sensitivity of precipitation to the added GCCN (i.e., precipitation susceptibility, So). The paper aims to show the observational evidence that the increased large-sized aerosols (GCCN) enhance precipitation in the warm marine boundary layer clouds from the precipitation susceptibility’s view. The results are expected to help understand the cloud lifetime effect better.

## Data and Method

### Data

Aircraft measurements (CIRPAS [Center for Interdisciplinary Remotely Piloted Aircraft Studies] Twin Otter [TO]) obtained during the E-PEACE are employed in this study. The E-PEACE was a targeted field campaign that occurred off Monterey, California, during July and August 2011, focusing on the responses of marine Sc clouds to the emitted aerosol perturbations of ship exhausts, smokes, and salts. The TO research aircraft was equipped with a vertically pointing cloud radar and various instruments that measure standard meteorological variables (e.g., temperature, winds, and liquid water content (LWC)) and properties of aerosols, clouds, and precipitation (Table 1). Detailed information on each instrument can be found in previous studies (e.g., Jung and Albrecht, 2014;Wang et al., 2014).

### Mathematical formulas and terms

The assessment of aerosol effects on precipitation is challenging as factors other than aerosols can modulate precipitation. To minimize the nonaerosol effects on precipitation, Feingold and Siebert (2009) proposed precipitation susceptibility (So), which estimates the effects of aerosols on precipitation while minimizing the effects of macrophysical factors (i.e., meteorology). It is defined as follows:

$S o = − d ln R d ln N d$
(1)

where R and Nd, respectively, indicate the precipitation rate and cloud droplet number concentrations at the cloud base. The liquid water path (LWP) is used as a fixed cloud macrophysical property in Eq. (1); Nd contributes to aerosol loading as aerosols serve as cloud condensation nuclei (CCN). Since Feingold and Siebert (2009) first proposed the precipitation susceptibility matrix, cloud condensation nuclei (CCN), aerosol optical depth, and cloud depth, H, have been used to calculate So depending on data availability. For example, So have been calculated from satellite data using an aerosol proxy (e.g., optical depth or aerosol number concentration) instead of Nd (Sorooshian et al., 2010); CCN has been used instead of Nd in a surfacebased observational study (Mann et al., 2014); H or both H and LWP have been used instead of LWP in an aircraft-based observational study (Terai et al., 2012). In this study, H was used as a fixed cloud macrophysical property because the aircraft carried the cloud radar that can detect the cloud tops but did not carry a radiometer that retrieves the LWP. Precipitation rate, R, cloud droplet number concentrations, Nd, and H were sampled while the aircraft flew near the cloud bases (cloud-base level-leg flight). The cloud-base level-leg flight usually lasts about 7-15 min with an aircraft speed of approximately 50 m s−1 . Dates and periods of cloud-base level-leg flights used for the analysis are listed in Table 2. So calculation is summarized in this study (for details, refer to Jung et al., 2016). So is calculated from Eq. (1) within a given interval of H, where H is chosen to contain a similar number of data points.

H was determined from the height difference between cloud tops and bases. The cloud radar determined cloud tops with a 3-Hz time resolution and a 5-mvertical resolution in height. The cloud bases were determined from the lowest heights where the vertical gradients of LWCs were the greatest from the LWC profiles. The LWC profiles were obtained (i) when the aircraft entered the cloud decks to conduct level legs and (ii) from the nearest one or two soundings to cloud-base level-leg flights. For the two soundings, the average of the two heights was used as the cloud-base height in this study (same as “cb-mean” in Jung et al., 2016). Generally, the heights approximately corresponded to the lowest heights that the LWCs exceeded by 0.01 gm−3 . So was also estimated using the cloud-base heights determined from the cloud-base level-leg flights to examine the sensitivity of So for the data used.

It should be noted that the susceptibility of the probability of precipitation (POP), Spop, was also used in some previous studies (e.g., Wang et al., 2012;Mann et al., 2014) to examine the aerosol effects on precipitation. The second indirect effect―from the extended cloud’s lifetime perspective―involves the increase of cloud fraction due to the increase of aerosol loading and may be well-represented with Spop. However, the second indirect effect―from the view of the suppressed precipitation due to the increase of aerosol loading―may better be represented by So relating to precipitation rate. Thus, we used So in this study. Further, 1-s data were used for the So estimates because the behavior of So was preserved regardless of data resolution (e.g., 1-second or averaged data over the e-folding time) (Jung et al., 2016).

## Results and Discussion

### Thermodynamic properties and cloud-seeding experiments

During the E-PEACE, more than 30 research flights (RFs) were conducted (Table 1 of Russell et al., 2013), and 13 flights sampled the typical coupled maritime Sc cloud decks among them; the details are summarized in Table 2. Cloud depths shown in Table 2 are calculated from the height differences between cloud tops (measured by cloud radar) and cloud bases. Cloud bases are averaged from the nearby soundings and cloud base heights that are identified from the vertical structures of LWCs (lowest height that the vertical gradient of LWC is the greatest) that the aircraft enters the cloud deck to conduct the cloudbase level-leg flight. The thermodynamic properties of marine Sc for the 13 flights are shown in Fig. 1; the potential temperature and mixing ratio were almost constant below the cloud deck, indicating a wellmixed marine boundary layer (MBL). The MBL depth was approximately 660 m. The vertical structure of LWCs showed that clouds were nearly adiabatic (Fig. 1c), and the maximum H was in the range of 600-650 m. During the E-PEACE, cloud-seeding experiments using salt powder (GCCN) were also conducted for nine flights. Owing to the complexity and difficulty of planning and fulfilling the effective seeding strategy under the proper meteorological conditions, only one case of August 3, 2011 (RF9) showed a remarkable impact of GCCN throughout the cloud depth (Jung et al., 2015). The seeding strategy and procedures are summarized in this study (for more details, refer to Jung et al., 2015). Milled salt with particles of 3-5-μm diameter was dispersed into homogeneous, unbroken Sc decks as the instrumented research aircraft was flying near the top of the cloud field (hereafter pre-seeding flight). The aircraft then sampled the downstream of the cloud fields initially seeded and advected (hereafter post-seeding flight). The typical flight patterns conducted during the E-PEACE are shown in Fig. 2 with an example of August 3, 2011, with the study area’s geographical location. Figure 2 shows that the aircraft flew out to the ocean first, then sampled the cloud decks along the coastline—northwest to southeast. Every single RF routinely conducted one or two vertical profiles (i.e., soundings) before and after the level-leg flights were conducted. On August 3, 2011, seeding was performed between 18:02 and 18:20 UTC (HH:MM) while the TO flew near the cloud tops. Before and after seeding, the aircraft sampled the cloud fields at three levels; near cloud bases, midclouds, and near cloud tops. The pre-seeding and postseeding flights correspond to 17:21-18:23 UTC and 18:49-19:17 UTC, respectively, in Fig. 2. The vertical structures of potential temperature, LWCs, wind speed and direction, and aerosol number concentrations from two soundings near 17:00 UTC are shown in Fig. 3. Thermodynamic properties of sub-cloud layers and cloud tops on August 3, 2011, are also shown in Fig. 3 as grey colors with blue squares. Figures 3 (b, e) show that the cloud bases and tops were approximately 300 and 650 m, respectively, and the cloud depths were in the range of 300-350 m. Potential temperatures were almost constant at ~287 K in the sub-cloud layer (Fig. 3a). Aerosol concentrations at sub-cloud layers were in the range of 200-300 cm−3 on average, with higher values near the surface (up to 700 cm−3 ) then decrease with heights (Fig. 3e). The northwesterly wind blew approximately 10 m s−1 on average nearsurface (~30 m above sea level), then increased with height (Figs. 3(c-d)).

### Characteristics of Nd and R

The daily averages of Nd and R for the 13 flights obtained during the cloud-base level-leg flights are shown in Fig. 4a. Generally, the daily-averaged R decreased as the daily-averaged Nd increased. The averages of Nd and R obtained from August 3, 2011, which showed the impact of GCCN throughout the cloud depth, was overlaid as different colors in Fig. 4(a-b). The mean Nd decreased from 162±56 cm−3 (bluish) to 77±50 cm−3 (reddish) (from pre-seeding to post-seeding flights) due to the enhanced collision and coalescence process. Accordingly, R increased from 0.97±3.2 to 3.1±7.1 mm day−1 (Fig. 4). Previous model studies suggested that the addition of GCCN has the greatest potential for altering cloud behavior in nonprecipitating clouds with high concentrations of smallsized aerosols (e.g., Feingold et al., 1999;Yin et al., 2000;Lu and Seinfeld, 2005;Zhang et al., 2006;Jensen and Lee, 2008). Figure 4(a) supports that the case of August 3, 2011 was ideal for showing the cloud-seeding effect. The details of changes in the droplet size, number concentrations, drizzle rate, and drop size distribution (DSD) are shown later in Fig. 5.

Scatter diagrams of ln(Nd) and −ln(R) are shown in Figs. 4(c-d). In Fig. 4c, So were calculated with 1-s data (grey dots) and daily-averaged values (red dots) for the 13 flights. The blue-dashed and red-solid lines correspond to So calculated using 1-s data and dailyaveraged values, respectively. The corresponding So were approximately 0.62 and 0.91, respectively, with the linear regression coefficients of 0.34 and 0.57, respectively. So were also calculated using 12 flights that excluded August 11, 2011, which showed heavy rain with small Nd and a substantially shorter e-folding time (e.g., a few s versus 3-4 min) (Fig. 4d). So were ~0.42 with 1-s data (grey) and ~0.70 with dailyaveraged values (pink) for the 12 flights. So was also calculated using data categorized by e-folding time. The e-folding time is the time scale for a quantity to decrease to 1/e of its previous value. If the data (e.g., precipitation data) correlated, it was irrational to use them to obtain the correlation coefficient. So obtained using the e-folding time (approximately 0.62), where a series of data lose correlation with each other, is added to Fig. 4(d). Figure 4(c-d) shows that So calculated with data obtained from cloud fields where precipitating and non-precipitating clouds coexist tends to be overestimated compared with So calculated with exclusively non-precipitating cloud fields (0.62 vs 0.42; 0.91 vs 0.70). In addition, So calculated using daily-averaged data rather than 1-s data or data categorized by e-folding time, the value tends overestimated (0.70 vs 0.42 or 0.62 for example in Fig. 4d).

Overall, the values of So were similar to those of Lu et al. (2009), who calculated So in the same NEP region for H varying from 200 to 600 m (So ~0.46- 0.48 using H and So ~0.60-0.63 using LWP). Earlier, we explained that the NEP Sc decks showed laboratorylike characters in which the background cloud property was similar over time. Therefore, clouds were considered to experience the same macrophysical properties. However, the cloud’s macrophysical properties might not be totally fixed throughout all flights, but rather slightly vary. These factors might explain the differences among So in Figs. 4(c-d).

### Changes in droplet properties

Changes in droplet size (effective diameter, D), number concentrations, Nd, drizzle rate, R, and drop size distribution (DSD) due to cloud seedings are shown in Fig. 5. The number concentration of cloud droplets was obtained using the cloud-aerosol spectrometer (CAS), and the drizzle rate was calculated using the cloud imaging probe (CIP) DSD, N(D), where u(D) is the fall speed of particle size, D (Rogers and Yau, 1989). The effective diameter was calculated using DSDs obtained from CAS and CIP by combining the CAS and CIP probe data to include cloud droplets, drizzle, and raindrop embryos.

In Fig. 5a, droplets crowded between 10 and 20 μm before seeding (bluish), whereas the droplets were widely distributed between 10 and 100 μm after seeding (reddish). The average number concentration of cloud droplets during the pre-seeding flight was about 160 cm−3 , but the numbers dropped to less than 100 cm−3 (~77 cm−3 ) after seeding (Fig. 5b). The drizzle rate was about 0.04mmh −1 before seeding, and it increased to 0.16 mm hr −1 after seeding (Fig. 5c). The changes in droplet size and number concentrations are shown in DSD (Fig. 5d). The DSD changes confirmed that the number of smaller-sized droplets reduced (in particular, droplets of D<20 μm), whereas the number of larger-sized droplets increased due to the seeding.

### Changes in precipitation susceptibility (So) - the seeding effect

To minimize the impact of macrophysical properties on the cloud-aerosol-precipitation interaction, So with a fixed cloud macrophysical property (e.g., H) was calculated. The scatter diagrams of ln(Nd) and −ln(R) for pre-seeding and post-seeding flights are depicted in Fig. 6 to show the precipitation susceptibility calculation procedure. In summary, a linear regression fit of ln(Nd) versus −ln(R) for a given interval of H indicated the value of So in Fig. 6. The nonprecipitating clouds sampled during the pre-seeding flights showed narrow distributions of cloud properties (Figs. 6f-6h). For example, Nd varied little, not providing sufficient variation for the reasonable estimates of So. In turn, So was not calculated for the pre-seeding clouds (Figs. 6f-6h).

So were calculated for the 12 flights of typical Sc decks and post-seeding flights (Fig. 7). Table 3 summarizes the statistics of So for the 12 and postseeding flights, including the intervals and averages (±1 σ) of H and So values as well as the number of data points used to calculate So. So were calculated with all available data (1-s data). Besides, So were calculated with the subset of data (with about half of the data) randomly sampled, which is a commonly used method to check the uncertainty of the calculated value. Three hundred data points—corresponding to about half of the total data points—were used to calculate the So, except for the largest H interval. The robustness of the calculated So was examined by repeating the process 1,000 times.

In Fig. 7, So calculated using the 12-RF dataset was almost constant at around So ~0.2-0.3 when the cloud depth was less than ~240 m, indicating that R was insensitive to aerosol burdens when H<~240 m. Once the clouds were deeper than ~240 m, R tended to be sensitive to aerosol burden until H ~350-380 m; So monotonically increased with an increase in H (i.e., ~0.7 increased in So per 100 m), illustrating the suppression of precipitation due to the increase of aerosol loading. Figure 7 also shows that R was most susceptible to aerosol burden changes when clouds are approximately 380-m deep, where H ranged between 150 and 420 m. Once the clouds were deeper than ~380 m, R became less sensitive to aerosol loading because there was ample precipitable liquid water available to precipitate. Therefore, changes (i.e., increases) in Nd contributed little to changes (decreases) in R. Such H-dependent So behavior agreed with the typical pattern of So previously observed and simulated in low, warm boundary layer clouds (Feingold and Seibert, 2009;Sorroshan et al., 2009, 2010;Jiang et al., 2010;Gettelman et al., 2013;Jung et al., 2016). For the post-seeding flight, So fluctuated around zero, regardless of H (Fig. 7, red). Such low and almost constant values of So in the precipitating clouds, as a result of GCCN seeding, indicated the possible reasons for the lower So in the higher LWP regime in previous studies (e.g., Mann et al., 2014;Terai et al., 2015). Interestingly, Fig. 7 shows how dramatically the So changes from non-precipitating to precipitating clouds; the high value of So in non-precipitation-dominating clouds reduced in precipitation-dominating clouds.

The addition of GCCN into the clouds, particularly in regions where Nd was high, produced precipitation more readily by enhancing the collision and coalescence process (Feingold et al., 1999;L’Ecuyer et al., 2009). Such model-based results were demonstrated in nature through the GCCN seeding experiments during EPEACE by comparing the changes of drop sizes, aerosol amounts, and DSDs before and after seeding. The current study further demonstrated the cloud lifetime effect by showing changes in the So pattern from non-precipitating to precipitating clouds due to cloud seeding.

So calculated using normalized H supported the previous results (Fig. 8). Figure 8 is the same as Fig. 7, except for the normalized H to use. Figure 8 is useful to examine the So behavior for the relative H. One can gain a generalized idea of how the clouds react with the aerosol amounts in a given area. For example, if clouds ranged from 300 to 1,300 m in a given area with similar cloud bases, aerosols would not impact precipitation initiation for cloud tops less than 640m (H<340 m in this case). Further, precipitation tended to suppress in regions where the clouds grew to 1,150 m (340 m<H<850 m); aerosols tended to enhance precipitation once clouds grew deeper than ~1,150 m (H>850 m). If one has the climatological cloud distribution for a given area, one can forecast the aerosol impacts on precipitation for the newly growing clouds.

## Summary and Conclusion

The second aerosol indirect effect (i.e., cloud lifetime effect) remains the center of the discussion, partly due to lack of observations of the cloud life cycle and partly due to the cloud problem. In this study, the precipitation susceptibility (So)—which minimizes the cloud problem—was calculated for the typical marine Sc decks and GCCN seeded clouds. So calculated from the typical coupled, well-mixed maritime Sc decks showed the typical So pattern, showing three regimes—low insensitive So, mid-range of So that showed an increase in So with aerosols, and high H of So decreased as aerosol increased. Moreover, the addition of GCCN to Sc cloud decks dramatically reduced So to nearly zero for all ranges of H, demonstrating the observational evidence of the second indirect effect.

The role of GCCN in clouds and precipitation is crucial as cloud amounts and albedo decrease as precipitation increases, and the chain processes can compensate for or offset global warming. Further, the GCCNs promoting precipitation in warm marine boundary layer clouds contribute to the moisture budget in the atmosphere and regulate the hydrological cycle. Although there is no consensus on whether the production of GCCN (not only the sea spray but also soluble dust particles) (e.g., Woodcock, 1952;Levin et al., 2005;Johnson, 1982;Rosenfeld et al., 2002) will increase or decrease in future climates; clearly, the direction and magnitude of GCCN production is an essential factor in current and future climate systems in terms of the hydrological cycle and radiative forcing in climate systems. GCCN from sea spray would have a strong link to near-surface wind speeds and the sea state. Therefore, the results further suggest that the response of precipitation to changes in GCCN concentrations should be considered for the accurate prediction of aerosol-cloud-precipitation interactions by climate models, as suggested by Jensen and Lee (2008).

## Acknowledgments

The author gratefully acknowledges the crews of the CIRPAS Twin Otter for their assistance during the field campaign. The author also thanks to anonymous reviewers for their constructive and comprehensive comments on the manuscript. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1F1A1053023).

## Figure

Vertical profiles of (a) potential temperature, (θ, K), (b) mixing ratio, (g kg−1), and (c) liquid water content (LWC, g m−3 ) obtained from 12 flights. The profiles of August 3, 2011, are overlaid as black colors.

(a) Geographical location of the E-PEACE field campaign with flight domain (red square); (b) flight paths; (c) time series of flight altitudes on August 3, 2011. Time elapses from bluish to reddish colors.

Profiles of (a) potential temperature (K), (b) LWC (g m−3 ), (c) wind speed (m s−1 ), (d) wind direction (degree), and (e) accumulation mode aerosol concentrations (#/cc) during the aircraft ascent (black) and descent (red) between 16:52 and 17:10 UTC (HH:MM). Aerosol concentrations obtained from the sub-cloud layer and above clouds are shown as grey colors. Blue squares indicate mean values.

(a) Cloud-base drizzle rate (Rcb) versus cloud droplet number concentration (Nd) for 13 flights during the E-PEACE field campaign; dots and crosses indicate the mean and median values, respectively; blue and red are flight data from the pre-seeding and post-seeding on August 3, 2011; lines indicate the one standard deviations (1σ). (b) Bluish and reddish dots indicate the individual overlaid with mean (±1σ) values for the pre-seeding and post-seeding flights. (c-d) Scatter diagram of ln(Nd) and - ln(R) for 13 and 12 flights; grey dots indicate individual 1-s data; red and pink dots indicate daily-averaged values; numbers on the upper right corner indicate the So and linear regression correlation coefficient (r); blue crosses indicate the cloud data averaged over the corresponding e-folding time; lines indicate the linear regression fits for the corresponding colored data.

Changes in (a) droplet size, (b) Nd, (c) R, and (d) DSD during the cloud-base level-leg flights on August 3, 2011. Data obtained from pre-seeding and post-seeding flights are shown as blue and red, respectively; the corresponding mean and median values are shown as square and cross symbols. DSDs are calculated from CAS (thin) and CIP (thick) probes. “BEFORE” and “AFTER” indicate pre-seeding and post-seeding flights, respectively. The figure is replotted by modifying Figs. 6 and 7 of Jung et al. (2015).

The ln(Nd) and -ln(R) diagram for each H interval for clouds sampled during the post-seeding flight (left, “AFTER SEEDING”) and pre-seeding flight (right, “BEFORE SEEDING”); So values are shown in the lower bottom right corner; drizzle rate, R, increases downward in the ordinate, and Nd increases toward the right in the abscissa.

So estimated with aircraft measurements for 12 flights of the typical maritime Sc clouds sampled during the E-PEACE field campaign. So is estimated with cloud bases that were determined from the averaged cloud-base heights from the nearby soundings and height that the aircraft entered the cloud deck to conduct the cloud-base level-leg flight. So are calculated using all available data (open square) and randomly subsampled (1,000 times) data (filled circles) for given H intervals. So calculated for the post-seeding flight are overlaid as red, labeled as AFTER. Horizontal and vertical bars indicate the ±1σ of H and So, respectively.

The same as Fig. 7, but H is normalized and two So estimates are shown. So values are estimated with the cloud bases determined from the averaged cloud-base heights from nearby soundings and height that the aircraft entered the cloud deck to conduct the cloud-base level-leg flight (square, same as Fig. 7). Further, So values are estimated from the height that the cloudbase level-leg flights were made (circle). Filled colors indicate the mean value of So calculated from the randomly subsampled cloud data. Vertical bars indicate the So±1σ.

## Table

Instruments used in this study

Dates and periods for the cloud-base level-leg flights used for the analysis

Data numbers and uncertainty of So for a given H interval (used in Figs. 7 and 8) for the 12 flights during the EPEACE

Data numbers and uncertainty of So for a given H interval for the post-seeding flight on August 3, 2011 during the EPEACE

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