Holographic measurements of inhomogeneous cloud mixing at the centimeter scale

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Science  02 Oct 2015:
Vol. 350, Issue 6256, pp. 87-90
DOI: 10.1126/science.aab0751

Cloud mixing and droplet evolution

When clouds mix with drier air because of atmospheric turbulence, some of the cloud droplets evaporate. Beals et al. developed an airborne holographic imaging system to look at changes in the spatial structure and sizes of these droplets (see the Perspective by Bodenschatz). Turbulent mixing of clouds with clear air caused dramatic fluctuations in the number density of water droplets but left their mean diameter essentially unchanged. This finding should help models better represent these hard-to-parameterize cloud processes.

Science, this issue p. 87; see also p. 40


Optical properties and precipitation efficiency of atmospheric clouds are largely determined by turbulent mixing with their environment. When cloud liquid water is reduced upon mixing, droplets may evaporate uniformly across the population or, in the other extreme, a subset of droplets may evaporate completely, leaving the remaining drops unaffected. Here, we use airborne holographic imaging to visualize the spatial structure and droplet size distribution at the smallest turbulent scales, thereby observing their response to entrainment and mixing with clear air. The measurements reveal that turbulent clouds are inhomogeneous, with sharp transitions between cloud and clear air properties persisting to dissipative scales (<1 centimeter). The local droplet size distribution fluctuates strongly in number density but with a nearly unchanging mean droplet diameter.

Clouds consist of only Embedded Image volume fraction of liquid water, yet this trace amount is crucial to the formation of precipitation and the transport of enthalpy, electromagnetic energy in both optical and thermal infrared bands, and even entropy within the atmosphere (13). To a large extent, the challenge of representing clouds in coarse-resolution weather and climate models is to capture the details of how turbulence transports and dilutes cloud water through mixing with their environment (4). Mass and energy conservation allows precise calculation of the final liquid water content after a cloud is diluted with clear, subsaturated environmental air. Liquid water content, however, scales as Embedded Image, where n is the droplet number density and d is the droplet diameter; due to complex turbulent interactions between droplets and the water vapor and temperature fields, it is by no means obvious to what extent reduction in Embedded Image results from relative changes in n and Embedded Image and how the answer may depend on the size of the averaging volume. For example, do droplets evaporate by uniformly reducing their size across the population, leaving n largely unchanged except through simple dilution, or, in the other extreme, does a subset of droplets evaporate completely, leaving the others in the volume unchanged, i.e., Embedded Image constant? These two limiting processes, proposed by Baker and Latham more than 30 years ago, are referred to, respectively, as homogeneous and extremely inhomogeneous mixing (5, 6).

As simple as the posed question sounds, it has been the source of controversy for several decades and has set a high bar for measurements of cloud particle size distributions. At its most basic level, the question is related to the sharpness of cloud boundaries and how droplet size and number density vary along those edges. More specifically, in situ cloud measurements have required averaging over long distances compared to the turbulent scales of a cloud boundary (712), thereby relying on the questionable assumption of ergodicity when translating to an ensemble view in theoretical or computational models (see the supplementary text) (13, 14). In this work, we overcame the large-scale spatial averaging problem by using an airborne digital in-line holographic system that images the three-dimensional (3D) structure within ~15-cm3 cloud volumes and provides size distributions of the Embedded Image droplets contained therein (1517). The approach allows us to probe the response of cloud droplets to turbulent mixing down to the smallest scales where kinetic energy is dissipated by viscosity (~1 to 10 mm). Essentially, it allows us to visualize the sharpness of cloud edges and the changes in droplet diameter near those edges without ambiguities introduced through spatial averaging.

The response to reduction in Embedded Image within Embedded Image space is of more than just academic interest because large-scale cloud properties like colloidal stability (18) and optical thickness (19) depend sensitively on both n and d. The magnitude and longevity of the problem are illustrated by Blyth (20), who in a review of the state of the field 20 years ago went so far as to speculate that without entrainment and turbulent mixing “many problems in cloud physics would have been more-or-less solved.” As a specific example, it is arguable that the microphysical response to entrainment directly influences the albedo response of the planet to aerosol perturbations (21). Jeffery (22) provided a scaling argument to demonstrate the importance of mixing for the shortwave optical depth Embedded Image, which, because the droplets are large compared to the wavelength, scales as Embedded Image. The response of Embedded Image to reduction in cloud liquid water content Embedded Image by evaporation can be expressed as a susceptibility Embedded Image. In the homogeneous limit where Embedded Image, this results in Embedded Image, and in the extremely inhomogeneous limit where Embedded Image, the susceptibility is Embedded Image. These are comparable to other indirect effect susceptibilities (see the supplementary text) (23) and suggest that the nature of mixing, and its representation in models, has a leading-order effect on the optical properties of clouds. Thermal infrared properties may be even more strongly influenced because of the absorption near cloud edge, where the imprint of mixing is most prominent (19).

Figure 1 (left panel) illustrates typical empirical evidence supporting the notion of inhomogeneous mixing at the macro scale, with wt varying nearly continuously between zero and the maximum for the undiluted cumulus cloud, but with Embedded Image jumping sharply from zero to a nearly constant value. The implication is that cloud dilution occurs primarily through reductions in the number density n. The lingering question, however, is whether this is rather an artifact of the measurement method, by which individual droplets are counted and sized as they cross a narrowly focused laser beam. To obtain a statistically robust estimate of the mean diameter, between 10 and 100 m of flight path must be traversed. Figure 1 (right panel) depicts the resulting dilemma: Suppose at cloud edge, there are filaments of undiluted cloud and homogeneously mixed cloud, in which droplet diameter has decreased in proportion with the mass fraction of entrained clear, dry air. The averaging instrument obtains an accurate measure of the reduction in n due to entrainment and mixing but measures aEmbedded Image that is strongly biased toward the value in the undiluted cloud (i.e., the great majority of droplets sampled are from undiluted cloud regions). It therefore remains unknown at what scale inhomogeneous mixing actually occurs or to what extent homogeneous mixing is masked by instrument sampling artifacts. To a large degree, this measurement challenge has motivated important new developments in cloud physics instrumentation over the course of at least two decades: for example, the use of high-speed optical counters that reveal the fine-scale spatial statistics of clouds (810, 2426) or optical methods for estimating droplet effective radius and liquid water content on 10-cm scales (27, 28). Most of these measurements have indicated a prevalence of inhomogeneous mixing. As pointed out by Burnet and Brenguier (9), however, these advances have still left the fundamental ambiguity as to whether the apparently inhomogeneous signature is real or an artifact of instrument averaging. The problem calls for an instrument capable not only of measuring locations of droplets on small scales but also of directly measuring the full droplet size distribution on those same scales.

Fig. 1 Relative constancy of cloud droplet diameter during entrainment and mixing and its possible bias from sampling and averaging.

(Left) Fluctuations in liquid water content Embedded Image and mean droplet diameter Embedded Image in a cumulus cloud, as sampled by an airborne droplet-counting instrument (DMT Cloud Droplet Probe). Data were obtained during the IDEAS project in November 2011, from the NSF/NCAR C130 (15). The data have a resolution (spatial averaging scale for droplet-by-droplet counting) of 20 m. Cloud liquid water content (red curve) varies widely between Embedded Image and nearly 1 g m–3, but mean droplet diameter (blue curve) is seemingly binary, jumping suddenly between Embedded Image and ~16 μm. (Right) A schematic view, not to scale, of droplets sampled by a single droplet detector (i.e., droplets intersected by the thin, red volume). The behavior observed in the top panel could be an artifact of instrument averaging over cloudy and clear regions within the 20 m needed to count enough droplets to estimate Embedded Image. The sampled number density n accurately accounts for the dilute regions, but the Embedded Image is strongly biased toward the value in the undiluted cloud regions.

We have developed an approach based on holographic imaging of cloud droplets within discrete volumes, which allows us to overcome the need for spatial averaging and the associated assumptions regarding statistical homogeneity and ergodicity (see the supplementary text). Individual in-line holograms encode the size and 3D position of an ensemble of hydrometeors in a localized volume illuminated by coherent light. That information is later extracted through digital reconstruction. The Holographic Detector for Clouds (HOLODEC) is an airborne instrument that takes snapshot holograms of all resolved particles in an approximately 15-cm3 volume (1517). The important result is that holography allows statistically robust cloud droplet size distributions to be determined for each hologram (or even for subvolumes within a hologram). The sampling strategy is in contrast to that of single-particle light-scattering techniques, which often require averaging over 10 to 100 m to build up a similar number of droplets for a statistically robust estimate of the size distribution. Digital holography provides a well-defined sample volume with particle size and 3D position recorded without coincidence effects. Thus, HOLODEC provides accurate (both in terms of single droplet measurement and in terms of statistical sampling) droplet size distributions representative of “local” (i.e., centimeter-scale), microphysical conditions relevant to diffusion growth and mixing.

We have used the HOLODEC instrument to investigate the variability of liquid water content and droplet size distribution on centimeter scales relevant to microphysical response to turbulent mixing. The data used in this study come from convective clouds sampled during two stages of the Instrument Development and Education in Airborne Science (IDEAS) field project (15). Figure 1 (left panel) is taken from a single cloud pass during IDEAS-2012 and illustrates the highly variable conditions on 20-m scales and above. Other cloud passes from both field projects exhibit qualitatively similar behavior. The holograms recorded provide an unprecedented view of the 3D distributions of cloud droplets at centimeter-to-micrometer scales within the cloud and the size distributions that result from droplets sampled on that scale. Figure 2 shows sample volumes typical for undilute (top) and dilute (middle and bottom) cloud regions. The dilute holograms are sometimes observed to be homogeneous in their spatial structure (middle) but sometimes are quite striking in their filamentary structure (bottom). The corresponding size distributions suggest that large drops remain within the clustered holograms, whereas more uniform evaporation has occurred within the homogeneous volumes. The filamented holograms provide direct and striking evidence for the persistence of sharp edges down to centimeter scales, consistent with turbulent scaling arguments (6, 11). For the observed turbulent conditions in these clouds, a transition scale below which homogeneous mixing should predominate is predicted to be on the order of several centimeters (10).

Fig. 2 Centimeter-scale measurements of cloud droplet spatial distributions and corresponding size distributions obtained with the HOLODEC instrument.

The volumes show examples of an undiluted cloud volume (top), a diluted but spatially uniform region (middle), and a diluted, strongly filamented cloud volume (bottom). Internal spatial inhomogeneity such as that illustrated in the bottom panel tends to occur more frequently near cloud edges (see the supplementary text). The size distribution for each hologram (color) is compared to an averaged size distribution from relatively undiluted holograms (solid line). Furthermore, the “local” size distributions obtained from individual holograms can be rather distinct from the spatially averaged distributions containing approximately the same number of droplets obtained from single-droplet-counting instruments (see the supplementary text).

The spatial distributions in Fig. 2 suggest that highly inhomogeneous mixing exists, so we consider to what extent this pervades the cloud. In Fig. 3, we look at the centimeter-scale size distributions across the entire two-cloud traverses by plotting the two variables contributing to liquid water content, n and Embedded Image (7, 9). Each point on the plot represents n and Embedded Image derived from counting and sizing droplets in a single hologram—i.e., in a ~15-cm3 volume with maximum dimension ~10 cm. The values are normalized by the corresponding averages of the 10 holograms with the highest droplet number density (i.e., Embedded Image and Embedded Image), such that undiluted cloud is assumed to lie at the point (1,1). Two theoretical curves are shown on the plot: the horizontal (solid) line at Embedded Image represents extremely inhomogeneous mixing—i.e., as clear air is entrained, a subset of droplets is completely evaporated, leaving the remaining droplet diameters unchanged. The curved (dashed) line represents homogeneous mixing, in which all droplets are assumed to evaporate in a uniformly and thoroughly mixed volume. Results from passes through the two clouds previously described are shown to illustrate that the trends are quite general. The data points in both examples show striking agreement with the inhomogeneous hypothesis, confirming for the first time from direct measurements of the droplet size distribution in localized volumes that clouds indeed have sharp edges down to centimeter scales. Apparently, even when the edges, which represent the signature of transient mixing events, eventually diffuse away, they do so after sufficient evaporation occurs that the majority of remaining droplets have relatively undisturbed diameter.

Fig. 3 Mean cubic droplet diameter Embedded Image versus cloud droplet number density n, measured with digital holography in two convective clouds.

Each point corresponds to a “local” Embedded Image and n obtained from individual, ~15-cm3 holograms. The clouds were sampled in (top) November 2011 from the NSF/NCAR C130 and (bottom) September 2012 from the University of Wyoming King Air research group (15). Mean diameter and number density are normalized by the least-diluted cloud values Embedded Image and Embedded Image, such that an undiluted cloud sample would lie at the position (1,1). The curved dashed line is the theoretical prediction for homogeneous mixing, and the horizontal solid line is the prediction for the extremely inhomogeneous mixing limit. The homogeneous mixing line is calculated based on measurements of temperature and water vapor concentration in the environment outside the cloud and in undiluted regions of cloud (15). For that calculation, total water content (vapor plus liquid) and liquid-water potential temperature are assumed to be conserved scalars during mixing (9, 28). For both clouds, the holograms display Embedded Image, confirming that inhomogeneous mixing persists down to centimeter scales, the dissipative scale of turbulence. The points in the second example do show a tendency to drop away from the inhomogeneous mixing line at maximum dilution, and this may be evidence for mixing with preconditioned air—e.g., a subsiding shell (30). For example, the points in the bottom panel are bounded by a homogeneous mixing line consistent with a mixture of approximately 10% environmental air and 90% saturated cloud air.

The holographic measurements show that turbulent clouds are inhomogeneous, with sharp transitions between cloud and clear-air properties persisting to dissipative scales (1 to 10 mm). As a result, the droplet size distribution fluctuates strongly in number density but with a nearly unchanging mean droplet diameter, down to the smallest turbulent scales. This 3D view of the cloud structure has several implications, including motivation for including the effects of microphysical mixing in subgrid-scale representation of entrainment in cloud models (13, 14, 29). This in turn will influence the modeled optical and dynamical cloud properties, along with their role in weather and climate (see the supplementary text). For example, the predominance of inhomogeneous mixing suggests that the optical depth susceptibility Embedded Image is closest to its maximum possible value of 1. The observations also add further plausibility to the hypothesis that mixing and the resulting evaporation can lead ultimately to enhanced droplet growth (18): Inhomogeneous response to mixing leaves droplets of the same diameter as in the undiluted regions of cloud but with considerably reduced competition for excess water vapor. Perhaps, however, the qualitative picture of clouds having sharp edges down to the centimeter scale is the most vivid impression to be taken from the work.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S10

References (3169)

References and Notes

  1. Materials and methods are available as supplementary materials on Science Online.
  2. Acknowledgments: We thank J. French and the aircraft staff for assistance with the instrument deployment on the University of Wyoming King Air research group. We thank the staff of the National Center for Atmospheric Research (NCAR) Earth Observing Laboratory for assistance with the instrument deployment on the NSF/NCAR C130. This project was supported by U.S. National Science Foundation grant AGS-1026123, by the U.S. Department of Energy as part of the Atmospheric Radiation Measurement Climate Research Facility, and by a NASA Earth and Space Science Fellowship. NCAR is sponsored by the U.S. National Science Foundation. Data are available according to instructions in the supplementary materials on Science Online.
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