Introduction

The concentration of water vapor in air is one of the most basic quantities in atmospheric science. Indeed, students in the discipline learn its various definitions almost immediately, which is not surprising, considering the fact that both the mean and fluctuations about that mean on a variety of time scales play key roles in determining Earth's weather and climate. As just two examples, the average concentration of water vapor determines its impact as a greenhouse gas while fluctuations about the mean are important when considering phenomena like propagation of electromagnetic radiation in the visible portion of the spectrum through the atmosphere. Both the mean and fluctuations can be important when considering aerosol activation and the growth of cloud droplets (Srivastava 1989;Kulmala et al. 1997;Shaw et al. 1998;Kostinski 2009;Krueger 2020;Chandrakar et al. 2020b;Anderson et al. 2023). Clearly, information on both mean and fluctuations is needed to understand the impact of water vapor in the atmosphere. In spite of its importance, the direct measurement of supersaturation under cloudy conditions remains elusive. Several field measurements exist; however, these measurements either temporally average out a fraction of the fluctuations based on the time response of the sensors (Gerber 1991) or are focused on the spatial variability of the supersaturation with unknown aerosol populations (Ditas et al. 2012;Siebert and Shaw 2017). Even in the more controlled conditions of the laboratory, it is easier to explore the humidity distribution under subsaturated or cloud-free conditions due to liquid water interfering with the measurement (Niedermeier et al. 2020;Anderson et al. 2021). In this paper we explore humidity fluctuations in clouds with a range of different aerosol concentrations.

The water vapor mixing ratio is defined as r ; m y /m a , where m y is the mass of water vapor in a volume of air and m a is the mass of dry air. Because three phases of water (gas, liquid, solid) coexist in the atmosphere, a second measure of water vapor abundance is also commonly used, the relative humidity or saturation ratio:

where e is the partial pressure of water vapor. The subscript s denotes a value taken in equilibrium with a plane surface of pure, liquid water at the temperature T. The temperature dependence of the saturation vapor mixing ratio r s is explicitly noted in the right-hand side of Eq. ( 1). S is a measure of how close the ambient water vapor concentration is to the concentration required for equilibrium with liquid water. Values of S above or below 1 can be interpreted as the thermodynamic forcing toward condensation or evaporation (Lamb and Verlinde 2011, p. 174).

Growth of a single cloud droplet from vapor is typically written in the form

where m d and r d are the mass and radius of the drop, respectively, r l is the density of liquid water, and G incorporates surface and heat transfer effects (Lamb and Verlinde 2011, p. 328).

Finally, S K is the saturation ratio at the surface of the droplet, where the subscript K is in reference to Köhler theory. The driving force for condensation (or evaporation) is the difference in the water vapor concentrations at the surface of the droplet and at infinity (Lamb and Verlinde 2011, p. 324). However, the historical development has been to replace that difference in water vapor concentrations with a difference in saturation ratios, which is what we adopt here. While Eq. ( 2) is straightforward for a single cloud droplet, it is usually applied to ensembles of droplets as well, which presents some difficulties. As a number of authors have noted (Srivastava 1989;Kulmala et al. 1997;Shaw et al. 1998;Kostinski 2009), S, on the right-hand side of Eq. ( 2), is ambiguous. The saturation ratio is almost certainly not uniform over a given volume of air; in fact, Eq. ( 2) depends on it. If aerosol particles are clustered, competition for vapor may deplete the local concentration of water vapor and thus S (Srivastava 1989;Shaw et al. 1998). Growing water drops release latent heat to the surroundings, increasing the local temperature, also reducing S (Kostinski 2009). In addition to effects from the presence of multiple droplets within the volume, clouds are ubiquitously turbulent, which induces fluctuations in the concentrations of scalars such as water vapor and temperature (Kulmala et al. 1997;Gerber 1991;Siebert and Shaw 2017). In short, there is no single value for S, as it varies as a function of spatial position and time due to a combination of effects.

Fluctuations in the saturation ratio are frequently quantified through the variance s 2 S , which has been shown to depend on the phase relaxation time t c and the Lagrangian correlation time t t (Chandrakar et al. 2016;Cooper 1989). Desai et al. (2018) showed that these time scales contribute to the variance of the saturation ratio in cloud conditions. They showed that fluctuations in the integral radius I (defined below) cannot be neglected in such conditions. The in-cloud variance is quantified as

where s cloud is the mean in-cloud supersaturation (s 5 S 2 1), s 2 S,moist and s 2 S,cloud are the variances of S in moist and cloudy conditions, respectively. The integral radius is I 5

, where r d is the droplet radius and n d is the droplet number concentration. Also, I is the fluctuating term of the integral radius, defined as I ; I 2 I, where I is the measured, instantaneous value. The phase relaxation time is t c 5 (4pD y I) 21 , where D y is the modified diffusion coefficient described in Cooper (1989). Equation (3) depends on the ratio of t t /t c , which is traditionally referred to as the Damk öhler number, Da. In the atmosphere, Da , , 1 and Da . . 1 describes the slow (clean) and fast (polluted) microphysics regimes. When t t /t c , , 1, which occurs when the droplet integral radius is small (e.g., low droplet number concentration, here referred to as clean), Eq. (3) implies that s 2 S,cloud ' s 2 S,moist , if we assume I 2 /I 2 has a similar value to what was reported in Desai et al. (2018). It suggests that in clean clouds, there is little buffering of the supersaturation field by droplet growth.

The behavior in the limit t t /t c . . 1 depends on the strength of the relative fluctuation of the integral radius I 2 /I 2 . If it is small, as in a spatially and temporally uniform field of droplets, then the t t /t c . . 1 limit implies s 2 S,cloud becomes vanishingly small. In this case, the supersaturation field is expected to be strongly buffered by highly responsive droplet growth and evaporation, resulting in a uniform distribution.

Our aim in this paper is to quantify the variability in S under cloudy conditions with varying levels of aerosol loading, and corresponding variations in clean to polluted cloud conditions. This will allow us to observe the extent to which buffering of the supersaturation distribution occurs, which contributes to understanding processes in the atmosphere. For example, the growth of cloud droplets is affected by that variability, which in turn alters the variability in S through the transfer of latent heat and water vapor. To do this, we use high-speed measurements of both the water vapor density and temperature with and without cloud formation in the Pi chamber. With this dataset, we are able to get the first high-speed measurement of S in a cloud, under a controlled laboratory conditions.

Methods

Measurements were made in the Pi chamber, which is described in detail in Chang et al. (2016). Here, we provide only a brief overview. The chamber is a turbulent Rayleigh-Bénard convection (RBC) cell in which the lower surface of the chamber is set to a higher temperature than the upper surface. These conditions induce turbulent mixing due to the buoyancy difference between warm and cool air. As the air mixes it results in fluctuations in the temperature and water vapor concentration. For the typical conditions we employ, the Rayleigh number in the chamber is ;10 9 . For all of the experiments reported here, the temperature difference (DT 5 T bottom 2 T top ) in the chamber was 16 K. The mean temperature was 208C, with T side 5 208C, T top 5 128C, and T bottom 5 288C. The surfaces of the chamber are wetted, such that the convection transports both heat and water vapor. In this paper we present measurements in moist and cloudy conditions in the chamber. Here, moist conditions refers to the case were the chamber is supersaturated, but there is no cloud formation due to lack of cloud condensation nuclei. In cloudy conditions, we inject size selected sodium chloride (NaCl) aerosols of diameter 130 nm into the chamber using a differential mobility analyzer (DMA; TSI model 3071). (Note that because of multiple charging effects, there is also a mode of particles with diameter of approximately 200 nm injected, but the magnitude of this mode is much smaller than the one at 130 nm.) By varying the number concentration of particles injected into the chamber, we can achieve droplet concentrations ranging from tens to hundreds of cubic centimeters. Note that the aerosol concentrations stated in this paper refer to the concentration of aerosol in the airstream injected into the chamber. For example, injecting 3.14 3 10 3 particles per cubic centimeter (particles cm 23 ) at 2 L min 21 (lpm) into the chamber would correspond to an addition of 2 particles cm 23 min 21 within the chamber volume provided the air is well mixed. While the bulk of the chamber is close to being well mixed, it does take some time before reaching that state. Since our injection is done at a single point, that area will see a slightly higher aerosol concentration than the rest of the chamber. Because of this point source injection, we will use the source injection rate as the distinction between different cases instead of the, perhaps more intuitive, chamber diluted injection rate.

We measured the water vapor mixing ratio, r, using a LiCor LI-7500A infrared hygrometer. It has a pathlength of '12.5 cm, and has an averaging time of 0.2 s. Occasionally a drop from the ceiling of the chamber may pass through the measuring path of the LiCor, causing the LiCor measurement to report a clearly erroneous data point. When this happened, we replaced the outlying point with the average of the data points immediately before and after the droplet passed through the LiCor. To best match the pathlength and temporal averaging of the water vapor measurement, we used a high-speed sonic temperature sensor (Applied Technologies Inc.) to measure temperature, T. The sonic temperature sensor was set to sample at 1 Hz and has a pathlength of '13 cm. The mean value of the sonic temperature sensor was calibrated to a collocated 100 V thin film, platinum resistance thermometer (RTD, Minco, S17624, 100 V 6 0.12%). The LiCor and the sonic high-speed temperature sensor were placed near the center of the chamber. The LiCor and sonic high-speed temperature sensor parallel were placed so the measuring paths were parallel and vertically separated by '3 cm.

Both the pathlength and temporal averaging of the sensors can artificially suppress measured fluctuations in r, T, and subsequently, the saturation ratio S. In our case, the path averaging has a larger effect on S than temporal averaging. Despite this averaging, our setup still captures a large portion ('81%) of the turbulent fluctuations. These issues are discussed in more comprehensive detail in Anderson et al. (2021).

We use the measured values of r and T to calculate the saturation ratio S, defined in Eq. (1). In practice, the saturation values in the equation are calculated from an approximation of the Clausius-Clapeyron equation, using the measured value of T (Lamb and Verlinde 2011). Measurements from subsaturated conditions (S , 1) are discussed in Anderson et al. (2021). Here we focus on differences between moist and cloudy conditions.

We also use r and T to calculate the moist static energy (MSE), defined as

where c p is the heat capacity of the air mass and l y is the latent heat of condensation. (Note that for our case, we have dropped the geopotential F from the definition of moist static energy since it is essentially constant over the volume of the chamber.)

The moist static energy is unchanged by condensation as energy is simply shuffled between the two terms on the right-hand side of Eq. ( 4). We use the MSE for several purposes. First, it ensures that we have thermodynamic consistency between various experiments over which the microphysical conditions are changing. Second, and related to the previous point, the value of MSE is used to ensure any change in S is due to the physics of cloud formation, and not entrainment of outside air into the chamber. Third, calculating the MSE from measured temperature and water vapor fields provides a "sanity check" that the observed shifts in water vapor mixing ratio are believable and are not likely the result of instrumental artifacts.

In cloudy conditions, the injected aerosol may activate and grow as cloud droplets until they are removed by sedimentation. In these conditions, we measure the cloud droplet size distributions with a Welas Digital 2000 optical particle counter, which is sensitive to size range of 0.6-40 mm in diameter. The size distributions were averaged over 100 s at a flow rate of 5 lpm.

Results and discussion

Our measurements cover a range of different microphysical conditions where the we take simultaneous measurements of r and T to get a high-speed measurement of S in cloudy conditions. Since the scalar measurements are qualitatively consistent for each case, we choose case 3 as an example of the systems behavior when transitioning to cloudy conditions. In this case the source injection rate was 145 000 particles cm 23 at 2 lpm. Time series of r, T, S, and MSE for a moist to cloudy transition are shown in Fig. 1. The blue line in the figure shows the measured or calculated values while the red line is a 5 min running mean. [Note that the data have been filtered to remove oscillations associated with the chamber controls, which are on the order of 10 min. See discussion in Anderson et al. (2021) for details.] The experiment begins by letting the chamber come to a dynamic equilibrium in the moist state. Until aerosol injection begins (shown with the vertical black line in all panels), the mean values of all four variables shown in the figure are roughly constant, with significant excursions above and below the mean, consistent with the fully developed turbulence in the chamber.

At '4000 s, NaCl aerosols are injected into the chamber, forming a cloud, marked by the first vertical black line in all four panels of the figure. Shortly after aerosol injection, there is a decrease in r and a corresponding increase in T from the latent heat of condensation. As expected, S decreases due to the combined changes of r and T as water vapor condenses to liquid. Also, as expected, the moist static energy is unchanged from moist to cloudy conditions. As mentioned previously, this provides strong confidence that our measurements of water vapor concentration and temperature are reliable over the range of microphysical conditions that has been explored. Upon cloud formation, the system begins to relax to a new dynamic equilibrium, as cloud condensation nuclei FIG. 2. PDFs for moist (blue line) and cloudy (red line) conditions for r, T, S, and MSE for the time series shown in Fig. 1. The shifts in r, T, and S and the lack of a shift in MSE are consistent with water vapor condensing onto the injected aerosol to form a cloud.

the probability density function (PDF) of r shifts to lower values, consistent with water vapor being removed from the volume as it condenses to cloud droplets. Similarly, the PDF of T shifts to higher values as the air in the volume is warmed by the release of latent heat. Combining the two effects, the saturation ratio is reduced, as expected. The moist static energy is essentially unchanged. For the cases shown here, the transition from moist to cloudy conditions does not dramatically change the variance of r, T, and MSE. In this instance, there is a slight decrease in the variance of S, although such a decrease is not seen in every experiment that we conducted.

As noted above, the data shown to this point have been for a moist to cloudy transition upon injection of approximately 145 000 particles cm 23 at 2 lpm into the chamber. We also conducted experiments in which the injection was approximately 10 4 , 5 3 10 4 , 10 5 , and 2 3 10 5 particles cm 23 at '2 lpm. The results are qualitatively similar over seven different experiments. (We repeated selected experiments, which is why experiments outnumber conditions.) We turn to a discussion of differences among these experiments by first establishing the baseline. The top panel of Fig. 3 is a plot of the PDFs of the saturation ratio S for all seven experiments for the time period approximately one hour before aerosol injection. The distributions for each day are in agreement, with the exception of case 7, when it is likely the chamber was slightly drier due to loss of moisture from the chamber or degradation of the filter paper used to hold moisture at the top, bottom, and sidewalls of the chamber. This demonstrates that our initial conditions before cloud formation are generally consistent.

The PDFs for the cloudy cases are shown in the second panel of Fig. 3. In every case, the introduction of aerosol particles induces a decrease in the saturation ratio, as condensation reduces the water vapor concentration and increases the temperature. As the concentration of injected particles increases, the saturation ratio shifts to lower values, though the variance of the distributions is approximately unchanged. Table 1 is a compendium of select values of parameters measured and calculated for all experiments.

A careful look at the PDFs in cloudy conditions highlights a limitation in the ability to measure the absolute magnitude of S. When the injection rate was 214 kpcc (case 1 in Fig. 3; see caption of Fig. 3 for the definition of kpcc), nearly all of the measurements fall below the saturation line, which cannot be physical because a cloud was formed at that time. As a result, the average saturation ratio must have an offset due to an offset in the measured water vapor concentration and/or temperature. Because we compensate for a potential offset in T by using an RTD [see Anderson et al. (2021) for details], the measurement of r is primarily responsible for the offset in S. The offset inherent to the measurement of r cannot be easily accounted for due to difficulties in calibration and a drift in the zero point (i.e., offset) of the LiCor. To address the offset in r, we increase every value of S (for all cases) by 0.041. This shift was chosen so that the mode of the PDF in the most polluted case is at S 5 1. The results of this shift are shown in the lower two panels of Fig. 3. We refer to data for which we have applied this procedure as compensated; for the remainder of the manuscript, we use the compensated values of S.

It is important to remember that the distributions S in a turbulent environment depends on the simultaneous fluctuations of r and T. To help visualize these fluctuations Fig. 4 shows a plot of the water vapor mixing ratio as a function of temperature for the moist (top panel) and cloudy (bottom panel) conditions shown in Fig. 1. In this figure, r was adjusted such that the data are consistent with the corresponding compensated distribution of S. The saturation mixing ratio is shown as the solid line in the figure, while the dashed lines shows the mixing ratio expected if the only process in the chamber were mixing of plumes from the top, side, and bottom saturated surfaces [see Shawon et al. (2021) for details]. The three lines shown here are for the sake of clarity. The red circles are averages of r as a function of T in 0.018C increments.

Consistent with Figs. 1 and 2, the mean values shift to a slightly higher temperature and lower water vapor concentration upon injection of CCN. One striking feature evident in Fig. 4 is the range of vapor mixing ratios for a given temperature. At 20.58C, there is a 1 g kg 21 spread in vapor mixing ratios, which is roughly consistent across the range of temperatures measured. In moist conditions a majority of the data points fall within the area formed by the mixing lines and no measurements fell above the upper mixing line. In cloudy conditions the majority of the measurements lie above the saturation mixing ratio, but the range of data points shows that a significant fraction of air within the chamber is subsaturated. Going from moist to cloudy conditions the range of values around the mean does not change, because the covariance and variances of r and T are unchanged after cloud formation. The scaled variances of r and T in moist and cloudy conditions are shown in Table 1.

The mean water vapor concentration in each temperature range (red circles) also shifts to lower values, though the slope of the line through those points (not shown) does not change appreciably upon cloud formation. In every case the slope of the red points is positive, which indicates the correlation between r and T is positive. For case 3 the cross-correlation coefficient between r and T was 0.5. The spread of measurements around these points shows there is a process in the chamber that decreases that correlation. The value of the slope can change depending on several factors (Chandrakar et al. 2020a) but in general it indicates the relative importance of r and T. In this case, the shallower slope shows that the temperature variability is relatively larger than the water vapor variability, which could be due to a slight subsaturation of one or more surfaces of the chamber. Because the slope is shallower than that of the Clausius-Clapeyron curve at the mean temperature, we expect that the warm boundary (bottom surface) is where the drying may have occurred.

While cloud droplet growth depends on S and S responds to this growth, the saturation field is a construct of the r and T fields. For a model to properly resolve the variability of S, it must account for the simultaneous fluctuations in r and T. An expression for the variance of S is shown in Kulmala et al. (1997):

where r and T are fluctuating terms (a primed quantity is the difference between a measured value and the mean), R is the universal gas constant, and l y is the latent heat of condensation. The equation shows s 2 S,calculated is determined by three terms: the normalized variance of r (term A), the scaled covariance of r and T (term B), and the scaled variance of T (term C). Values of these terms, calculated from our data, in moist and cloudy conditions are shown in Table 1. Term A is the smallest; B and C are comparable in magnitude, but on average C . B. Compared to the measured value of s 2 S , s 2 S,calculated overestimates the variance in all cases by '10%. A small difference between s 2 S and s 2 S,calculated is expected because Eq. ( 5) ignores all terms with a higher order than the variance, e.g., the skewness and kurtosis. Notably the skewness of S can be negative, which could explain the why the calculated variance is higher than the measure variance. Perhaps unexpectedly, s S , cloud ' s S , moist in every case. TABLE 1. The statistics for each day in moist and cloudy conditions. The variance of S (s 2 S ) was derived from the data shown in the third panel of Fig. 1 after the high-pass filter was applied. Going from moist to cloudy conditions s 2 S does not appreciably change. The three different terms in Eq. ( 5) are independently calculated from r and T, where term A is the water vapor variance term, term B is the covariance term, and term C is the temperature variance term. s 2 S,calculated is the variance of S calculated using terms A, B, and C with Eq. ( 5). s 2 S,calculated is comparable to the measured variance, but slightly overestimates the variability of S.

Case 1 2 3 4 5 6 7 Moist s 2 S (310 4 ) 1.87 1.47 2.18 1.56 1.45 1.74 1.66 s 2 S,calculated (310 4 ) 1.97 1.54 2.29 1.62 1.52 1.81 1.72 A (310 4 ) 1.48 1.30 1.55 1.33 1.23 1.32 1.38 B (310 4 ) 2.11 1.81 1.95 2.05 2.09 1.93 2.09 C (310 4 ) 2.53 2.01 1.95 2.28 2.33 2.37 2.46 Cloud Injection rate (kpcc) 214 6 2 196 6 3 145 6 5 103 6 3 5 46 4 5 06 2 1 06 2 s 2 S (310 4 ) 1.95 1.59 1.96 1.31 1.31 1.83 1.94 s 2 S,calculated (310 4 ) 2.04 1.67 2.04 1.37 1.37 1.91 2.02 A (310 4 ) 2.16 1.95 1.71 1.62 1.70 1.49 1.36 B (310 4 ) 1.97 1.39 1.54 2.07 2.41 1.63 1.81 C (310 4 ) 2.04 1.72 1.98 1.89 2.15 2.13 2.46

In cloudy conditions one may expect condensation and evaporation to buffer fluctuations in S by decreasing S in regions of high supersaturation and increasing S in regions of subsaturation. If this buffering effect is the only process at play in cloudy conditions, we would expect the cloud of data points in the lower panel of Fig. 4 to converge toward the saturation line, indicating an increase in the cross correlation of r and T. Because the overall size of the cloud of points in Fig. 4 and the value of the B term (the covariance term) in Eq. ( 5) are comparable when transitioning from moist to cloudy conditions, we know the buffering effect cannot be the only process that influences s 2 S,cloud . A closer look at term B in Eq. ( 5) shows any process that decorrelates r and T will increase s 2 S,cloud , provided it does not change s 2 r or s 2 T . In both the Pi chamber and the atmosphere, the correlation of r and T decreases when water condenses onto (or evaporates from) droplets, which must compete with the buffering effect. In this set of measurements, because s 2 S,cloud ' s 2 S,moist , we suggest any buffering of supersaturation fluctuations by droplets must be offset the by decorrelation of r and T, though this may not be true in general.

Because our measurements cannot cover every set of microphysical conditions, in which regime does the buffering effect balance the decorrelation effect? To address this, we consider the range of Damköhler numbers achieved in the experiments.

To estimate the Damköhler number, we solve Eq. ( 3) for Da and use our measured values for s 2 S,moist , s 2 S,cloud , and s cloud 2 : Da 5 t t t c 5 s 2 S,cloud 2 s 2 S,moist s cloud 2 I 2 I 2 2 s 2 S,cloud :

In this expression the only term we were not able to calculate was I 2 /I 2 , but if we consider the possible values for this ratio we can put an upper bound on Da. In Eq. ( 6), Da has a maximum value when I 2 /I 2 5 0. In this case we find Da maximum ' 1. and Da is small, we confirm our assumption made in the introduction. These values indicate the conditions in the Pi chamber, for the aerosol injection rates achieved here, lie in a range that covers part of the slow microphysics regime and the transition between the fast and slow regimes (where Da ' 1).

Using the values of the Damköhler number derived in the previous paragraph and our cloud droplet measurements shown in Fig. A1 in the appendix, we can calculate the phase relaxation time (t c ) and put an upper bound on the Lagrangian correlation time (t t ). In Fig. 5 we show most of the values for t c are below 5 s, with the exception of the lowest injection rate. t c is calculated based off of Cooper (1989) and the cloud droplet sizes shown in the supporting information. As the injection rate increases, t c is observed to decrease. This relationship is a result of the injection rate controlling the concentration of aerosols and cloud droplets. As the injection rate increases, the competition for water vapor between droplets causes the mean radius to decrease, resulting in longer droplet lifetimes, increased number concentrations, and a larger integral radius. With the values we have derived for t c , and the range of values of Da 5 t t /t c derived in the previous paragraph, we find t t Շ 3:2 s. This result compares favorably to the value reported in Desai et al. (2018).

Atmospheric implications

The measurements of the variability of supersaturation presented in this work provides unique opportunity to systematically FIG. 5. The phase relaxation time (t c ) for the individual injection rates.

study the behavior of the S distribution under varying microphysical cloud conditions. We found the aerosol concentration changes the mean of S, but not the variance. By using collocated, highspeed measurements of T and r, we were able to determine the relative contributions of the variances and covariance of these two scalars. When the variances of r and T are scaled as in Eq. ( 5), the contribution from water vapor was found to be slightly less important than that from temperature. A positive correlation was found between r and T, which is consistent with the behavior of a moist convection chamber. Deviations from the ideal case can be attributed to drying of one or more surfaces in the chamber. These measurements show the in-cloud variability of S is higher than expected in clean clouds, which is important for determining aerosol activation and the cloud droplet size distribution for this type of cloud.

In situ measurements of marine boundary layer clouds have shown that they are typically in the fast microphysics (Da . 1) regime, but that the neighborhood of Da ; 1 is commonly achieved, especially in drizzling clouds (Desai et al. 2019). Over the range of aerosol injections rates in this study we found Da Շ 1, so we have explored from the slow microphysics regime (Da , , 1) to the transition regime. Our measurements, reported in Table 1, show variance of S is effectively the same before and after cloud formation. Initially this result may be surprising because it is typically assumed that the presence of cloud droplets will act as a buffer for the extreme values of the saturation ratio distribution. We suggest the release of latent heat during the phase transformation opposes the buffering effect, by decorrelating r and T, thereby increasing the variance of S. Our results imply these two effects are comparable in the slow microphysics regime. In the fast microphysics (Da . . 1) regime the denominator in Eq. (3) becomes significant, leading us to believe the buffering effect becomes dominant, dampening saturation ratio variance. We might expect, therefore, that only in the fast microphysics limit is the concept of saturation adjustment, as commonly used in models, an appropriate approximation.

We show the variability of S remains after cloud formation in clean clouds but the importance of these fluctuations is determined by the strength of those fluctuations and by S which is described using three regimes in Prabhakaran et al. (2020). They show fluctuations are likely to play a significant role in activation when s S,cloud is on the same order as or larger than S 2 1. In the atmosphere, this would typically exclude strong convective updrafts and very clean conditions. Instead the variability in S, and by extension the effects of turbulence, would be strongest where S is near saturation, such as in regions of relatively weak forcing, like weak updrafts or in radiative fogs, or in regions with strong entrainment such as near cloud edges, or in very polluted conditions where the cloud droplet number is high. It remains a challenge to explore the distribution of S under these kinds of conditions, even in the laboratory, and certainly in the atmosphere. As methods are developed that allow S to be measured in the fast microphysics regime, the onset of buffering effects can be further explored.

APPENDIX

Mean Droplet Diameter and Liquid Water Content

Upon cloud formation in the chamber, water vapor condenses, decreasing the mean vapor concentration. Liquid water is stored in the cloud until the droplets are removed by diffusing to the walls, being sampled out of the chamber by the Welas to measure the droplet size distribution, or through gravitational settling. Settling is the dominate removal mechanism for cloud droplets in the chamber. As Fig. A1 shows, the injection rate of aerosol particles into the chamber, which controls the number of cloud droplets formed, has a monotonic relationship with the liquid water content (LWC) of the cloud, at least in the range of injection rates we have studied. At low injection rates, the cloud droplets have a larger mean diameter (see right axis in the figure) and are removed quickly by gravitational setting, resulting in a lower LWC. As the number of CCN increases, the resulting droplets compete for water vapor, decreasing the mean diameter, consistent with previous results from the chamber (Chandrakar et al. 2016).

If we were to create a heavily polluted cloud in the chamber, we would expect a cloud that contains a large number of small droplets with low settling velocities. As this hypothetical cloud was formed r would decrease as water vapor condenses onto aerosols. Because the small droplets are removed slowly, we would expect the total amount of condensed water to be stored in the cloud, causing Dr ~LWC, where Dr 5 r moist 2 r cloud . In clean clouds, like the ones we are looking at in this study, it is not immediately apparent whether this relationship holds due to the rapid removal rate of large droplets with fast settling velocities. Our measurements show the decrease in the water vapor concentration (DN y ) corresponds to a oneto-one increase in the liquid water content of the cloud, shown in Fig. A2. It should be noted that the water vapor concentration is the same measurement as r, only converted to the same units as the LWC.