High-resolution lidar observations of sedimentation-induced size sorting of droplets near a laboratory cloud top

Significance

Our understanding of cloud microphysical properties at centimeter scales remains incomplete because of limited observations. Here, high-resolution lidar observations of clouds in a convection chamber show that although the cloud is homogeneous in the bulk region, it is inhomogeneous at centimeter scales near the top. The topmost cloud layer is dominated by entrainment, diluting cloud droplets directly, below which is a transition region where droplet sedimentation causes a size-dependent reduction of droplet concentration. This sedimentation-induced size sorting of droplets occurs on scales smaller than those typically used in cloud-resolving models, and it can play a crucial role in cloud evolution and radiative properties.

Abstract

Cloud optical properties and precipitation, which are crucial to weather and climate, are strongly influenced by cloud microphysical properties that are still poorly understood. Here, we develop a high-resolution time-correlated single-photon-counting lidar and apply it to observe cloud microphysical properties at one-centimeter range resolution in a convection chamber under well-controlled conditions. Together with concurrent in-situ measurements and theoretical analysis, our lidar observations indicate that although turbulent mixing tends to homogenize the cloud in the bulk region, entrainment and sedimentation cause inhomogeneities in droplet concentrations near the cloud top. Specifically, the topmost region is directly affected by entrainment, and lidar profiles show clear evidence of entrained air and detrained cloud filament. The transition region below exhibits vertical size sorting of cloud droplets caused by sedimentation. Our results suggest that using a single sedimentation velocity for all cloud droplets, as is done in many atmospheric models, overlooks key physics relevant to the microphysical structure near the cloud top. Our conceptual model used to describe these measurements can serve as a step toward improving the current modeling of processes in the cloud top region.

Cloud tops play a crucial role in reflecting sunlight and driving the exchange of mass and energy with the clear air above (1). Physical processes in the cloud top region, such as entrainment (2), sedimentation (3), phase change (4), and radiative cooling (5), can modulate cloud microphysical properties, which has a further impact on cloud optical properties and precipitation efficiency. In particular, entrainment and mixing can cause inhomogeneities in cloud properties at centimeter scales near the cloud top (6), while sedimentation can remove liquid water from the cloud-top entrainment zone and thus decrease the entrainment rate (3). These processes and their interactions can have a profound impact on cloud microphysical structure (7), cloud evolution (2), and aerosol–cloud interactions (8, 9). Despite its importance, the cloud-top region is not fully resolved even in high-resolution cloud models, and thus there is a strong need for the development of parameterizations that can accurately represent the governing physical processes there (10). However, our knowledge of cloud-top properties is far from complete, mainly because of limited observation capabilities at fine (i.e., $\sim$1 cm or less) scales.

In-situ instruments can provide measurements of cloud microphysical properties near the cloud top, but they could disturb the surrounding flow, thus affecting nearby properties, and they typically cannot provide information on spatial variability of cloud properties (e.g., profiles). Remote instruments overcome these limitations by profiling cloud properties in a nonintrusive manner (11). Specifically, lidar, which transmits periodic laser pulses and receives photons backscattered from cloud droplets, is ideal for cloud observations because cloud droplets with radii of a few micrometers can efficiently scatter visible and near-infrared light. However, conventional lidars, whether ground-based, airborne, or spaceborne, typically have range resolutions of a few meters or more, which are too coarse to observe cloud microphysical properties at fine scales.

Advanced lidars equipped with short-pulse lasers and time-correlated single-photon counting (TCSPC) detectors can resolve targets down to centimeters or even millimeters (12–15). These advanced techniques have been applied to topics such as single-photon imaging, forestry mapping, archaeology site surveillance, fluorescence lifetime measurement, and non-line-of-sight imaging (16–19). Recently, a ground-based vertically pointing TCSPC lidar was developed to observe atmospheric clouds at a resolution of 10 cm (20). The backscatter profiles from this lidar resolved the air–cloud transition zone within the cloud base and thus allowed the estimation of the droplet concentration there (14). However, this lidar cannot profile the cloud top because the light attenuates significantly within a few tens of meters above the cloud base, whereas an airborne or spaceborne high-resolution lidar would not be able to provide high temporal evolution of the cloud-top structure because of the fast-moving platforms.

One way to explore cloud-top structures at fine scales is to generate clouds in a laboratory cloud chamber where they can be produced and maintained under well-controlled conditions. Here, we develop a high-resolution TCSPC lidar with centimeter-scale range resolution and apply it to profile steady-state clouds in a convection cloud chamber. Unlike most of the previous convection chamber experiments in which the cloud was fully confined in a rigid box, in this study, a 16.5-cm-diameter opening is introduced at the top of the chamber (much larger than the laser beam width of $\sim$2 mm), through which the lidar profiles the cloud from above. The opening is also large enough that thermodynamic fields in the region probed by the laser beam can be considered independent of the surrounding rigid top surface. This is because the advection time scale ($\tau$) is 1 to 2 s (i.e., the time needed for the flow to pass the opening region, calculated as the diameter of the hole divided by the mean flow speed) and the turbulent energy dissipation rate ($ϵ$) is $\sim$10 cm²s⁻³ in the Pi Chamber. Therefore, the turbulent diffusion length scale is ${(ϵ{\tau }^3)}^{1/2}$$\sim$ 3 to 5 cm, which is thicker than the thermal boundary layer that exists in Rayleigh–Bénard convection, typically less than 1 cm in the Pi Chamber (21). So, there is plenty of time for the sharp wall-induced boundary layer to dissipate and to equilibrate to the local “open” boundary layer. This opening results in a sharp clear–air–cloud interface where entrainment occurs naturally.

In this study, we investigate cloud-top physics under well-controlled laboratory conditions using a high-resolution single-photon counting lidar. Our experiment focuses on specific key physical processes (specifically entrainment and sedimentation), rather than attempting to exactly simulate what occurs in a natural cloud. For example, processes such as cloud-top radiative cooling and the entrainment of various types of aerosol particles from cloud top, which also play important roles in natural clouds, are not considered in the experiment. Our results reveal that entrainment and sedimentation-induced droplet size sorting are key processes influencing cloud-top microphysical properties at centimeter scales. We interpret our experimental findings in conjunction with idealized turbulence and microphysics models.

Results

Lidar Observation of Laboratory Cloud at Centimeter Scales.

Experiments were conducted in the Pi Convection-Cloud Chamber, which has a cylindrical internal shape with a radius of 1 m and a height of 1 m, and thus a volume of $\pi$ m³. The Pi Chamber generates a turbulent and supersaturated environment through Rayleigh–Bénard (RB) convection by maintaining a warm, humid bottom surface and a cold, humid top surface (22). Clouds are formed when dry aerosol particles injected from the side wall at mid-plane (Fig. 1) activate to form cloud droplets, which then grow by condensation in the supersaturated environment and are finally removed by sedimentation. Steady-state conditions are reached when the formation of cloud droplets via activation is balanced by the loss of droplets via sedimentation. Detailed specifications of the Pi Chamber experiments are provided in Materials and Methods.

Fig. 1.

Schematic figure of the experimental setup. The chamber is maintained at a warm&humid Bottom surface and cold&humid Top surface. A steady-state cloud is formed and maintained by the continuous injection of aerosol particles from the side. The lidar is placed on Top of the chamber and looks downward through a 16.5-cm-diameter opening. Cloud droplet size distributions are measured by WELAS optical particle counter.

A high-resolution TCSPC lidar situated at the top of the chamber is pointed downward through a 16.5-cm-diameter opening at the center (Fig. 1 and Movie S1). This lidar, developed specifically for these chamber observations, emits short pulses of 515-nm wavelength light at 15 MHz and receives backscattered photons along the beam path. A schematic of the lidar design is shown in SI Appendix, Fig. S1, and the technical specifications of the lidar are provided in Materials and Methods and SI Appendix, Table S1. The range resolution of the lidar is 1.2 cm (SI Appendix, Fig. S2), which is two to three orders of magnitude less than that of traditional lidars. The operating technique of this TCSPC lidar also differs from that of traditional lidars in that it receives at most one backscattered photon from each laser pulse because of the combination of the short transmission path and the dead time of the detector. Detecting these “first-arriving photons” is an integral component of “first photon imaging,” where the distribution of the first detected photon is utilized to recover the spatial structure of the target with very low photon flux in the presence of high background noise (23, 24). The profile of first-arriving backscattered photons is the same as the traditional lidar backscatter profile under our experimental conditions in which the probability of receiving a backscattered photon from a lidar pulse is much less than unity (SI Appendix, Fig. S3).

The temperatures of the bottom, sidewall, and top surfaces were kept at 29 °C, 20 °C, and 11.5 °C, respectively. Dry monodisperse sodium chloride (NaCl) particles with mobility radii of 65 nm (selected by a differential mobility analyzer; see Materials and Methods for details) were injected into the chamber. Six experiments were conducted, each with a different aerosol injection rate (${\dot{n}}_{\mathit{in}}$) but with the same chamber boundary conditions (Table 1). Each experiment had three phases, each lasting 20 min: spin-up, steady-state, and cloud-collapse. Continuous aerosol injection lasted for 40 min, with the first 20 min serving as spin-up to ensure that the cloud reached steady-state conditions. During the steady-state phase (the next 20 min), droplet size distributions (DSDs) for radii between 0.3 and 20 $\mathrm{\mu }$m were measured at 1 Hz using a Welas-2000 optical particle counter with a 2300P sensor head. After that, aerosol injection was stopped and the cloud dissipated through sedimentation. Lidar observations were conducted in all three phases, with profiles of backscattered photons determined at one-second intervals. Background and range corrections were applied to the raw photon signals, and the resulting background- and range-corrected backscattered photon signals were binned to a range resolution of 1.2 cm, referred to as the lidar signals (in the unit of m²) throughout the text (Materials and Methods). The time evolution of the lidar signal profile confirms that the clouds reached steady-state conditions after the 20-min spin-up period and fully dissipated within 20 min after stopping aerosol injection (SI Appendix, Fig. S4).

Table 1.

Cloud droplet number concentration ($n_d$), mean radius ($r_d$), and liquid water content ($q_l$) in the steady state at six different aerosol injection rates (${\dot{n}}_{\mathit{in}}$)

${\dot{n}}_{\mathit{in}}$ (cm−3s−1)	nd (cm−3)	rd (μm)	ql (g m−3)	σ (m−1)	β (m−1 sr−1)
0.27	52.4	8.40	0.26	0.033	1.82 $\times$ 10−3
0.53	127	7.15	0.36	0.055	2.96 $\times$ 10−3
0.80	181	6.65	0.41	0.066	3.58 $\times$ 10−3
1.06	284	6.05	0.47	0.086	4.60 $\times$ 10−3
1.86	641	5.40	0.72	0.151	8.05 $\times$ 10−3
2.65	925	4.90	0.77	0.180	9.56 $\times$ 10−3

Extinction and lidar backscatter coefficients ($\sigma$ and $\beta$) are calculated from the Mie theory using the in-situ measured droplet size distributions (SI Appendix).

In-situ measurements during the steady-state phase (Fig. 2A and Table 1) show that higher ${\dot{n}}_{\mathit{in}}$ result in narrower droplet size distributions, higher droplet number concentration ($n_d$), greater liquid water content ($q_l$), and smaller droplet mean radius ($r_d$). These behaviors are consistent with previous laboratory experiments (25), numerical simulations (26, 27), and theoretical investigations (28). The values of $n_d$ varied from $\sim$50 cm⁻³ at the lowest injection rate to $\sim$1,000 cm⁻³ at the highest injection rate, covering the range that is typically observed in atmospheric clouds. The corresponding lidar signals (Fig. 2B) are greater in magnitude at larger values of ${\dot{n}}_{\mathit{in}}$, and the shapes of the profiles vary with ${\dot{n}}_{\mathit{in}}$. Specifically, the lidar signals in the top 0.1 m of the cloud increase roughly linearly with in-cloud depth, with the slope increasing with increasing ${\dot{n}}_{\mathit{in}}$. In contrast, the lidar signals in the lower part of the chamber decrease roughly linearly with in-cloud depth, with the magnitude of the slope increasing with increasing ${\dot{n}}_{\mathit{in}}$. In the transition region between, the enhancement of the lidar signals just above the mid-plane (near 0.4 m) is caused by the formation of cloud drops on freshly injected aerosol particles that are transported by the carrier flow toward the center where they are illuminated by the laser (Fig. 1A). In the following section, the relationship between the lidar signals and cloud microphysical properties in each of these regions is investigated.

Fig. 2.

(A) The probability density functions (PDF) of mean droplet size distributions (based on the representation $d{n}_d/dr$) averaged over the 20-min steady-state period for different aerosol injection rates (${\dot{n}}_{\mathit{in}}$). (B) Profiles of background- and range-corrected lidar signals in the cloud layer for different values of ${\dot{n}}_{\mathit{in}}$. The solid lines are the simulated lidar signals calculated under the assumption that the cloud is homogeneous in the chamber. (C) Similar to (B) except only the Upper part of the chamber (between 0 and 0.2 m) is shown. The solid curves are the simulated lidar signals calculated under the assumption that the droplet number concentration increases with in-cloud depth due to sedimentation in a turbulent environment based on Eq. 4. The curve for ${\dot{n}}_{\mathit{in}}=0.27$ cm⁻³s⁻¹ is the best fit, while curves for other ${\dot{n}}_{\mathit{in}}$ are predicted using the same fitting parameter. (D) Similar to (C), except lines between 0 and 0.1 m represent the best-fit lidar signals calculated under the assumption that the droplet number concentration increases linearly with in-cloud depth due to entrainment. Simulated lidar signals in the transition region between 0.1 and 0.2 m are similar to (C): The curve for ${\dot{n}}_{\mathit{in}}=0.27$ cm⁻³s⁻¹ is the best fit, while curves for other values of ${\dot{n}}_{\mathit{in}}$ use the same fitting parameter. Triangles denote the predicted lidar signal calculated with size-independent droplet sedimentation, and circles with black outlines denote predicted lidar signals calculated with a size-dependent droplet sedimentation.

The Relationship Between Lidar Observations and Cloud Microphysical Properties.

The profile of the first-arriving backscattered photons along the beam path, which is the same as the profile of lidar backscattered power ($F$) in our experiments (SI Appendix), is described by the lidar equation (29):

$$\begin{array}{c}\hfill F(z)=\frac{C\beta (z)exp\left[-2{\int }_{-z_0}^z\sigma (z)dz\right]}{{(z_0+z)}^2},\end{array}$$ [1]

where $z_0=0.55$ m is the distance between the lidar and the cloud top, $z$ is the in-cloud depth (measured from the top of the cloud, with $z=0$ at cloud top), $\beta (z)$ and $\sigma (z)$ are the lidar backscatter and extinction coefficients along the beam path, respectively (SI Appendix), and $C$ is a constant that depends on the properties of the lidar system such as the laser power, overlap function, and quantum efficiency of the detector. This equation relates measured lidar signals to cloud optical properties, i.e., $\beta (z)$ and $\sigma (z)$, which depend on wavelength and on cloud microphysical properties, i.e., $n_d$ and $r_d$.

Downward-looking lidar signals from a homogeneous cloud, with uniform $\beta$ and $\sigma$, would exhibit a maximum at the cloud top and a monotonic decrease with in-cloud depth according to Eq. 1. Moreover, under our chamber conditions where $\sigma z\ll 1$ (Table 1), expansion of Eq. 1 as $F(z){(z_0+z)}^2\approx C\beta (1-2\sigma z)$ shows that the (range-corrected) lidar signals should decrease linearly with in-cloud depth. The observed lidar signals (Fig. 2B) do exhibit this linear behavior, but only in the lower part of the chamber. Linear fits to the lidar signals between 0.5 m and 0.9 m from the cloud top (lines in Fig. 2B) based on the lidar equation (Eq. 1), where $C$ is a fitting parameter and $\beta$ and $\sigma$ are calculated from the measured droplet size distribution (Table 1), show excellent agreement with observations in the lower half of the chamber, suggesting that the cloud is homogeneous in this region. However, this agreement does not extend to the upper half of the chamber, indicating that cloud is not homogeneous there. A theoretical model is introduced below to attempt to explain this behavior.

There are several physical processes that could contribute to vertical inhomogeneity in droplet size distribution near the cloud top, such as turbulence transport, droplet sedimentation, and entrainment. To examine the effects of these processes, we first consider a simple scenario in which all droplets have the same radius and the sedimentation is balanced by turbulent transport (steady-state condition),

$$\begin{array}{c}\hfill K\frac{d{n}_d}{\mathit{dz}}+n_d{v}_d=0,\end{array}$$ [2]

where $K$ is the turbulent eddy diffusivity and $v_d$ is the sedimentation velocity. Similar equations have been used to study the vertical transport of aerosol particles in turbulent open-channel flow (30) and in the atmospheric boundary layer (31). In these canonical turbulent flows, $K$ is parameterized in terms of $z$, and thus $n_d$ can be obtained analytically. However, the parameterization of $K$ in terms of $z$ for RB convection has not been reported.

Here, we assume $K=v_{a}z(1-z/H)$, where the constant $v_a$ characterizes the strength of the turbulence, $z$ is the depth from the cloud top, and $H$ is the height of the chamber. This parabolic turbulent diffusivity profile is adapted from the open-channel flow (30, 32), which is the simplest functional form that allows the diffusivity to be a maximum in the center of the flow and reach zero at both boundaries, capturing the relevant physics of turbulent mixing in a convection chamber, as well as in a stratocumulus cloud with a strong inversion.

The analytical solution of Eq. 2 in the upper part of the chamber ($0<z<H/2$) is

$$\begin{array}{c}\hfill n_d(z,r_d)=n_d^{\ast }(r_d){\left[\frac{z}{H-z}\right]}^{v_d(r_d)/v_a},\end{array}$$ [3]

where $n_d^{\ast }(r_d)$ is the number concentration of droplets of radius $r_d$ at the reference height $z=H/2$. The droplet number concentration near the cloud top according to this expression increases with in-cloud depth at a rate that depends on $r_d$, and the relevant quantity controlling the vertical profile of droplet number concentration is the exponent $v_d(r_d)/v_a$, the ratio of droplet sedimentation velocity to characteristic turbulent velocity, which is analogous to the Rouse number (30, 33). The sedimentation velocity of cloud droplets is given by Stokes’ Law, $v_d\propto r_d^2$, and thus

$$\begin{array}{c}\hfill n_d(z,r_d)=n_d^{\ast }(r_d){\left[\frac{z}{H-z}\right]}^{k{r}_d^2},\end{array}$$ [4]

where $k$ is a parameter that depends on the coefficient for Stokes drag and $v_a$. A consequence of this result is that smaller droplet sedimentation velocity (i.e., smaller $r_d$) or stronger turbulent mixing (i.e., greater $v_a$ or smaller $k$) leads to 1) a more rapid increase in number concentration with in-cloud depth near the cloud top and 2) a more uniform concentration profile in the bulk region.

The extent to which the cloud droplet number concentration profile given by Eq. 4 yields the lidar signal profiles near cloud top is examined below with the assumption that the size-dependent reference $n_d^{\ast }(r_d)$ is the same as the in-situ measured DSDs (Fig. 2A). The value of $k$ in Eq. 4 is obtained by minimizing the squared difference between the observed and simulated lidar signals between 0 and 0.2 m below the cloud top (above the region affected by aerosol injection) for ${\dot{n}}_{\mathit{in}}=0.27$ cm⁻³s⁻¹, and this optimal $k$ is used to calculate profiles of DSDs for other ${\dot{n}}_{\mathit{in}}$, from which the resulting lidar signal profiles are calculated based on Eq. 1. These simulated lidar signal profiles (Fig. 2C) do increase with increasing in-cloud depth, but they are considerably larger than the observed ones, especially in the upper 0.1 m of the cloud, indicating that sedimentation and turbulent transport alone cannot explain the observed lidar signals there.

Entrainment, which occurs near the center of the chamber at the cloud top through the 16.5-cm-diameter opening (Fig. 1A) (34, 35), provides another mechanism that must be considered in the topmost cloud layer. Time series of the lidar signal anomaly—defined as the difference between the lidar signal and the mean lidar signal in the steady-state phase—show clear evidence of entrainment (blue spikes below the cloud Top in Fig. 3A). The decreases in lidar signals just below the cloud top are strongly correlated with the enhancement in lidar signals above the cloud top caused by the detrained cloud filament. In another experiment with a similar setup, an image of a vertical sheet illuminated by a green laser from below clearly illustrates the entrainment of air and detrainment of cloud filaments (Fig. 3B and Movie S2). Particle image velocimetry (PIV) observations in a small region near the cloud top demonstrate that entrainment and detrainment there are driven by wind shear at centimeter scales (Fig. 3 C and D and Movie S3).

Fig. 3.

(A) Time series of profiles of lidar signal anomaly (difference between the instantaneous lidar signal and the mean lidar signal averaged in the 20-min steady-state phase) for ${\dot{n}}_{\mathit{in}}=2.65$ cm⁻³s⁻¹. (B) Camera image of entrainment and mixing near the cloud Top. A green laser sheet projected upward illuminates the cloud from the Bottom, and the camera looks downward through the Top-Center opening. The corresponding video is in Movie S2. (C) Camera image of entrainment region observed by Particle Image Velocimetry (PIV) system $\sim$5 cm below the cloud Top at the Top-Center opening. (D) Retrieved air velocity based on PIV observations. The corresponding video for (C and D) is in Movie S3.

The effect of entrainment on droplet number concentration near the cloud top (i.e., between 0 and 0.1 m) is investigated using a simple model in which droplet number concentration increases linearly with in-cloud depth: $n_d(z,r_d)=k^{\prime }z{n}_d^{\ast }(r_d)$. This simple model is supported by recent chamber experiments that indicate that the mixing of entrained air near the cloud top is inhomogeneous, implying that the main effect of this mixing is a decrease in the droplet number concentration with little change in the mean droplet radius (34). The simulated lidar signals calculated using the value of $k^{\prime }$ resulting from minimizing the squared difference between the observed and simulated lidar signals now agree well with the observed lidar signals in the topmost cloud layer (Fig. 2D), indicating that entrainment is the dominant process affecting the droplet number concentration (and thus the lidar signals) there.

The direct influence of entrainment becomes less important further from the cloud top, and sedimentation and turbulent transport are expected to be the key factors that control cloud droplet size distributions, and thus the lidar signals, below the topmost entrainment-dominated region. This hypothesis is examined using a simple model in which droplet sedimentation is balanced by turbulent transport, such that droplet number concentration increases with in-cloud depth in the transition region (i.e., between 0.1 and 0.2 m to avoid the region influenced by aerosol injection) according to Eq. 4. The optimal $k$ is again obtained by minimizing the squared difference between the observed and simulated lidar signals for ${\dot{n}}_{\mathit{in}}=0.27$ cm⁻³s⁻¹, but only for $0.1<z<0.2$ m, and this value is used to calculate DSD profiles for other ${\dot{n}}_{\mathit{in}}$, from which the corresponding lidar signals are calculated. There is fair agreement between the calculated and observed signals in this region (Fig. 2D), and the discrepancy may come from additional influences from aerosol injection or the inaccurate expression for the turbulent eddy diffusivity used in the analytical model. Nevertheless, it is encouraging to see that the mean simulated lidar signal in the transition region agrees well with observations (circles with black outlines in Fig. 2D). Taking into account the size dependence of the sedimentation velocity is necessary. If it were assumed that droplet sedimentation is size independent (i.e., no size sorting) and droplet number concentration profiles follow $n_d^{\ast }(r_d){[z/(H-z)]}^{\alpha }$, where $\alpha$ is the only unknown parameter affecting $n_d(z)$ profiles, the lidar signals would be significantly smaller than observations especially at higher aerosol injection rates (triangles in Fig. 2D). These results indicate that our analytical model and Eq. 4 capture the essential physics below the entrainment-dominated region: The size-dependent droplet sedimentation sorting controls the vertical profile of cloud droplet size distribution in the transition region.

Discussion and Atmospheric Implications

In this study, we develop a high-resolution time-correlated single-photon counting lidar to observe cloud properties at centimeter-scale resolution, which is not achievable using traditional in-situ or remote sensing methods. We prove that the observed profile of first-arriving photons matches the traditional lidar backscatter profile at low photon rates, as in our experiments. This study combines high-resolution lidar techniques with first-arriving photon statistics to investigate cloud microphysical properties at centimeter scales under well-controlled laboratory conditions.

A key result of this study is that the lidar signals decrease linearly with in-cloud depth in the lower part of the chamber ($z>0.5$ m) at a rate that agrees with lidar signals calculated from in-situ observations of cloud microphysical properties (i.e., $n_d$ and $r_d$), indicating that the cloud is homogeneous in the bulk region—a common assumption made in theoretical or box models to represent clouds in a convection chamber (28). Another key result is that lidar signals increase with in-cloud depth in the upper part of the chamber, indicating a corresponding dependence of cloud microphysical properties on in-cloud depth there. The linear increase in lidar signals in the topmost cloud layer ($z<0.1$ m) can be well simulated by assuming that the droplet number concentration increases linearly with in-cloud depth because of dilution and evaporation caused by the entrainment. Both time series of lidar signal anomaly and camera observations provide direct evidence of entrained air and detrained cloud filament near the cloud top. Also note that the entrainment effect exists on a vertical length scale of $\sim$10 cm, more than a factor of 10 larger than the thermal and water vapor boundary layer that exists in Rayleigh–Bénard convection, which is known to be less than $\sim$1 cm thick, confirming that results reported here are not caused by wall-induced sharp gradients. Finally, the lidar signal profiles in the transition region (0.1 m $<z<$ 0.2 m, between the entrainment-dominated topmost cloud layer and the turbulent-transport-dominated bulk region below) suggest that droplet sedimentation is the dominant factor that decreases droplet number concentration near the cloud top where turbulence is relatively weak. This size dependence of droplet sedimentation (i.e., sedimentation sorting) plays an important role in controlling the vertical profile of droplet size distribution near the cloud top in the Pi Chamber.

Our results suggest that sedimentation becomes significant for size sorting when the nondimensional Rouse number, the ratio of droplet sedimentation velocity to characteristic turbulent velocity, is equal to or greater than unity. This underlying physical mechanism revealed by our experiments is widely applicable and supported by other studies. For example, sedimentation-induced size sorting of large raindrops has been recognized by radar observations for decades (36). Both lab experiments and numerical simulations show that droplet sedimentation can transport cloud water across the cloud-clear air interface, resulting in anisotropy of small-scale turbulence due to evaporative cooling (37). Small ice particles can be trapped in turbulent eddies, if their terminal velocities are smaller than or equal to updraft velocity (38). Previous studies, mainly based on numerical simulations (e.g., refs. 39–41), have shown that droplet sedimentation can change cloud microstructures; however, few studies have focused on the cloud top region. Our high-resolution lidar observations show observational evidence of droplet size sorting near the cloud top boundary that is generated at the cloud–clear–air interface in our idealized laboratory conditions.

We argue that sedimentation sorting is also important in controlling cloud microphysical properties near the top of atmospheric clouds. To demonstrate that this is the case, we calculate the in-cloud depth (i.e., distance from cloud top), $z_{\chi }$, at which the number concentration of cloud droplets of a given radius decreases to a given fraction ($\chi =n_d(z_{\chi })/n_d^{\ast }$) of that at the midpoint of the cloud ($z=H/2$). The ratio of this depth to the thickness of a well-mixed layer (e.g., $H=1$ m for the Pi Chamber or $H\sim 1$ km for the atmospheric boundary layer) is calculated from Eq. 3 as

$$\begin{array}{c}\hfill \frac{z_{\chi }}{H}=\frac{{\chi }^{v_a/v_d}}{1+{\chi }^{v_a/v_d}},\end{array}$$ [5]

where $v_a$ is the characteristic vertical air velocity in the mixed layer and $v_d$ is the droplet’s terminal velocity. This ratio, shown in Fig. 4 for the Pi Chamber using $v_a=0.05$ m s⁻¹, and for a typical stratocumulus-topped boundary layer using $v_a=0.5$ m s⁻¹ (42), depends strongly on cloud droplet radius. For example, the number concentration of cloud droplets with radii around 5 $\mathrm{\mu }$m decreases to 90% of that in the bulk region (i.e, at the midpoint) within 0.1$\sim$0.2 m from the cloud top in the Pi Chamber, but it is fairly uniform near the top of the stratocumulus. In contrast, the number concentration of cloud droplets with radii around 10 $\mathrm{\mu }$m exhibits a strong vertical variation in the Pi Chamber, dropping to 90% of that in the bulk region very near the midpoint of the chamber, whereas it decreases to 90% of that in the bulk region within a few to tens of meters from the cloud top in stratocumulus clouds.

Fig. 4.

The ratio of in-cloud depth at which the droplet number concentration less than 90% of its value at the midpoint of the cloud ($z_{90}$) to the thickness of the mixed layer ($H$) as a function of droplet radius based on Eq. 5 with $v_a$ equal to 0.05 m s⁻¹ and 0.5 m s⁻¹ for chamber ($H\sim 1$ m) and stratocumulus ($H\sim 1$ km) conditions, respectively.

Cloud-top entrainment can cause the droplet size distribution profile to deviate from the idealized shape expected from sedimentation-induced size sorting alone. For example, entrained dry air can lead to dilution and evaporation of cloud droplets, and thus decrease the droplet number concentration near the cloud top. Entrained aerosols can activate as cloud droplets, and thus enhance droplet number concentration. Despite the complexity and interactions of physical processes at the cloud top, we argue that sedimentation-induced size sorting establishes an idealized baseline for the cloud top microstructure, while entrainment determines which region of the cloud top can be affected.

Sedimentation sorting not only controls cloud microphysical properties near cloud top where they are directly impacted by entrainment, but it can also have a profound impact on cloud macroscopic properties and cloud evolution. Large-eddy simulations of stratocumulus clouds demonstrate that droplet sedimentation removes liquid water near the cloud top and thus reduces the entrainment rate by suppressing evaporative cooling and radiative cooling (3, 43). Direct numerical simulations of the cloud-top mixing layer produce an even stronger decrease in entrainment rate resulting from droplet sedimentation (44, 45). This sedimentation-entrainment effect is crucial to the response of cloud liquid water path to an increase in aerosol concentration (35, 46). Sensitivity studies from climate models also show that increasing droplet sedimentation velocity decreases cloud albedo susceptibility (9). However, cloud top is not adequately resolved in regional and climate models, and droplet sedimentation, even if included in these models, does not have the sorting effect (i.e., a single sedimentation velocity is assumed for all cloud droplets when using the bulk microphysics schemes) (47). Results in this study indicate that droplet sedimentation sorting near the cloud top can influence cloud microphysical properties at centimeter scales. An idealized model used to interpret these measurements can serve as a step toward improving our understanding of the vertical variation of cloud droplet size distribution near the cloud top caused by the joint effects of entrainment, turbulent transport, and sedimentation.

Materials and Methods

Pi Chamber Experiments.

The Michigan Tech Pi Chamber has been used to investigate aerosol–cloud–turbulence interactions under well-controlled laboratory conditions (25). The Pi Chamber forms a turbulent cloud through Rayleigh–Bénard convection by maintaining a warm, humid bottom surface and cold, humid top surface. The mixing of warm saturated air rising from the bottom and cold saturated air sinking from the top creates a supersaturated environment because of the nonlinear relationship between saturated water vapor pressure and temperature (i.e., Clausius–Clapeyron equation) (48). A cloud is formed when aerosol particles introduced into the supersaturated environment activate to form cloud droplets. By maintaining the chamber boundary condition and continuously injecting aerosol particles, a turbulent cloud can maintain a steady-state condition for hours, allowing cloud microphysical and optical properties to be measured accurately and repeatedly (25).

In our experiments, all surfaces were covered with wet fiber paper, and moist convection was held for eight hours to ensure stable temperature conditions before aerosol injection. Dry sodium chloride (NaCl) particles were generated by an atomizer and a dryer. A differential mobility analyzer was used to select particles with a mobility radius of 65 nm. The flow rate of aerosol-laden air into the chamber was held at 2 L per minute.

Time-Correlated Single-Photon Counting Lidar.

We designed a time-correlated single-photon counting (TCSPC) lidar for chamber observations, enabling remote measurements of cloud microphysical properties at the centimeter scale without disturbing the flow. The primary tool for capturing photons is a single-photon avalanche diode (SPAD), essentially a semiconductor diode that is reverse-biased above its breakdown voltage threshold for achieving single-photon sensitivity. The schematic of the TCSPC lidar used in this study is shown in SI Appendix, Fig. S1 with its key parameters listed in SI Appendix, Table S1. The TCSPC lidar operates with a customized, passively mode locked Ytterbium-doped fiber laser (YDFL) at 1,030 nm, later frequency doubled to 515 nm, that emits pulses of width 30 ps at a repetition rate of 15 MHz. A high-speed biased photodetector detects 1% optical power from the YDFL to provide a low jitter electrical reference signal, serving as the reference clock for the entire lidar system. The lidar has a collimated beam diameter of 2.2 mm that is guided through an off-axis parabolic mirror that also serves to collect backscattered photons. The profile of backscattered photons along the beam path can be reconstructed from the histogram of the photon arrival time measured by a Geiger-mode Silicon Avalanche Photodiode (MPD) and time-tagger (Swabian). The arrival time of each detected photon is recorded at 10 ps resolution with respect to the reference clock. The timing resolution of the entire lidar system is 80 ps (full width at half maximum calibrated in the laboratory; SI Appendix, Fig. S2), thus giving a range resolution of 1.2 cm, which is primarily limited by the timing jitter of the single-photon avalanche photodiode (Si-SPAD).

In our experiments, profiles of backscatter photons were output at one-second intervals. Background and range corrections were applied to the raw data. The background signal was determined as the value that gives the least squares difference between the raw lidar signal for ${\dot{n}}_{\mathit{in}}=0.27$ cm⁻³s⁻¹ and the theoretical prediction based on Eq. 1, with $\sigma$ and $\beta$ calculated from in-situ measured droplet size distribution (SI Appendix). The same background signal was used to correct other raw lidar signals at other aerosol injection rates. The range correction was performed by multiplying the background-corrected lidar signals with the square of the distance from the lidar, resulting in a unit of m². The background- and range-corrected lidar signals (referred to as the lidar signals for simple throughout the text) were used for further analyses in this study.

Particle Image Velocimetry (PIV) Observation of the Cloud Top.

We used Particle Image Velocimetry (PIV) to get 2-Dimensional velocity fields in the upper part of the chamber (20 cm $\times$ 20 cm area), which also includes the bottom portion of the opening. A 10 cm $\times$ 10 cm piece of the glass window was replaced with a piece of ITO-coated glass and maintained at a temperature slightly greater than that in the chamber to avoid condensation on the window and allow better visualization. A vertical sheet of the 532-nm wavelength laser light was generated using a 300 mW continuous laser and a Powell lens of 30° fan angle to illuminate cloud droplets and capture images at a pixel resolution of 130 $\mathrm{\mu }$m at 60 frames per second using a Sony-$\alpha$7 III digital camera. All images were preprocessed (contrast-stretching, background removal, and thresholding) before PIV analysis. Further, we have used an FFT window deformation algorithm from PIVlab (49) in 3 passes with interrogation areas (in pixels) of 256 $\times$ 256, 128 $\times$ 128, and 64 $\times$ 64 with window overlap of 50%, yielding a 2-D velocity field at a spatial resolution of 4.16 mm and a temporal resolution of 16.66 ms.

Supplementary Material

Appendix 01 (PDF)

Movie S1.

Video of the laser beam viewed from the side during the experiment.

Movie S2.

Video of entrainment and mixing near the cloud top.

Movie S3.

Video of the zoom-in entrainment region observed by Particle Image Velocimetry (PIV) system and the retrieved air velocity.

Data, Materials, and Software Availability

NPZ file and python code have been deposited in Michigan Tech Research Data Sharing Center (https://digitalcommons.mtu.edu/all-datasets/63) (50).