Laboratory Simulations Show Diabatic Heating Drives Cumulus-Cloud Evolution and Entrainment

Laboratory simulations show diabatic heating drives cumulus-cloud evolution and entrainment

Roddam Narasimhaa,1, Sourabh Suhas Diwana, Subrahmanyam Duvvuria,b,2, K. R. Sreenivasa, and G. S. Bhatc

aJawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India; bIndian Institute of Technology Madras, Chennai 600036, India; and cIndian Institute of Science, Bangalore 560012, India

Contributed by Roddam Narasimha, August 3, 2011 (sent for review June 16, 2011)

Clouds are the largest source of uncertainty in climate science, mining the evolution and entrainment dynamics of cumulus and remain a weak link in modeling tropical circulation. A major clouds. challenge is to establish connections between particulate microphysics and macroscale turbulent dynamics in cumulus clouds. Background Here we address the issue from the latter standpoint. First we The ability to simulate cloud processes under controlled and show how to create bench-scale flows that reproduce a variety repeatable conditions in the laboratory has long been recognized of cumulus-cloud forms (including two genera and three species), as a potentially valuable aid in studying cloud physics and dy- and track complete cloud life cycles—e.g., from a “cauliflower” con- namics. Many laboratory studies have been directed toward gestus to a dissipating fractus. The flow model used is a transient understanding the effect of small-scale turbulence on droplet plume with volumetric diabatic heating scaled dynamically to simu- microphysics (5, 9), among other issues. Recent experiments on late latent-heat release from phase changes in clouds. Laser-based a jet of moist air in a cloud chamber (11) have shown that the small-scale turbulence at the cloud-clear air interface is aniso- diagnostics of steady plumes reveal Riehl–Malkus type protected tropic. In another laboratory study (12) cloud-top entrainment cores. They also show that, unlike the constancy implied by early induced by radiative effects in stratiform clouds was simulated. self-similar plume models, the diabatic heating raises the Taylor None of the experiments devised to date, however, has been entrainment coefficient just above cloud base, depressing it at able to shed light (9) on the interaction of microphysics with higher levels. This behavior is consistent with cloud-dilution rates such cloud-scale turbulent processes as entrainment in cumulus found in recent numerical simulations of steady deep convection, clouds. In the present work we describe an apparatus capable of and with aircraft-based observations of homogeneous mixing in simulating such processes in the laboratory. This apparatus clouds. In-cloud diabatic heating thus emerges as the key driver in differs from others in use in two essential ways. First, it generates cloud development, and could well provide a major link between externally controlled amounts of volumetric heat within the flow, microphysics and cloud-scale dynamics. thereby decoupling heat release from phase change; secondly, it permits working with a single-phase “cloud fluid” (water in the ∣ ∣ ∣ cloud fluid dynamics off-source heating anomalous entrainment present instance), enabling us to focus on the essential macro- turbulent mixing scale physics of cloud flows. Laterally entraining turbulent plumes and thermals (Fig. 1 A–C) “ louds have been termed the big bad player in global warm- have been proposed in the past as physical models for cumulus- ” Cing (1) and are listed among the most urgent scientific pro- cloud flows, often employing self-similarity ideas (13–16). Such blems requiring attention by the Intergovernmental Panel on models are severely limited (17) and stand discredited by obser- Climate Change (2); more effective cumulus parameterization vations (especially in shallow cumuli), as they overpredict en- schemes can significantly improve predictions of the Indian mon- trainment rates and underpredict cloud-top height (18–20). soons. In particular, convective clouds (3) represent a set of com- These discrepancies, which have been collectively referred to as plex interactions among microphysics, flow turbulence, and radi- entrainment “anomalies” (10), have so far remained without a ation (4). They involve multiple phases, some of which change satisfactory dynamical explanation. This failure was in part due into each other releasing or absorbing considerable quantities to the assumption of a self-similarity that is not applicable to of heat, whereas many (including aerosols) affect radiative trans- cloud flows (16). Furthermore, these models could not account fer. Much attention has recently been devoted to investigating for the Riehl–Malkus protected cores (21) observed in midtropo- the interaction between fine-scale cloud turbulence and water- spheric clouds. Alternative proposals, such as episodic vertical droplet distribution and growth, and between cloud and radiation mixing (22, 23) and shedding thermal (16) models, have been (2, 4–6). However, cloud-scale dynamical processes, in particular found to be applicable primarily close to the cloud top (16, 24, the entrainment and mixing that affect microphysics (2), rain for- 25). Some recent studies (25–27) show that lateral entrainment mation (7), and cloud lifespan, remain puzzles despite numerous rates in cumulus clouds are large near cloud base and drop studies over the last five decades. To this day there are no satis- significantly at higher altitudes. Again no available cloud model factory fluid-dynamical models for cloud flows, and entrainment adequately explains these observations. continues to remain a matter of deep concern (8). In fact, the Herein we propose [extending earlier work on steady flows connections between cloud fluid dynamics and microphysics pose (10, 28, 29)] the transient plume subjected to off-source diabatic a major scientific challenge (9). heating as an appropriate low-order physical model for nonpre- Here we show how a variety of observed cumulus-cloud types (sometimes even shapes), and their associated life cycles, can be Author contributions: R.N., S.D., K.R.S., and G.S.B. designed research; R.N., S.S.D., S.D., and successfully simulated in the laboratory. This capability enables G.S.B. performed research; S.S.D. and K.R.S. contributed new reagents/analytic tools; R.N., direct measurement of entrainment rates using laser-Doppler S.S.D., and K.R.S. analyzed data; and R.N., S.S.D., K.R.S., and G.S.B. wrote the paper. and particle-image velocimetry. The data so obtained exhibit the The authors declare no conflict of interest. so-called anomalous entrainment characteristics (10) that have 1To whom correspondence should be addressed. E-mail: [email protected]. remained serious problems in cumulus-cloud modeling. Analysis 2Present address: California Institute of Technology, Pasadena, CA. of the data suggests that in-cloud diabatic heating, including its This article contains supporting information online at www.pnas.org/lookup/suppl/ variations in time and altitude, can play a central role in deter- doi:10.1073/pnas.1112281108/-/DCSupplemental.

16164–16169 ∣ PNAS ∣ September 27, 2011 ∣ vol. 108 ∣ no. 39 www.pnas.org/cgi/doi/10.1073/pnas.1112281108 Downloaded by guest on September 30, 2021 pose represents a considerable enhancement in capability over the original version (10) which was intended chiefly for investigating steady flows. The off-source diabatic heating is achieved through ohmic losses generated in the plume fluid, which is water rendered electrically conducting (“active”) by addition of acid (see Materials and Methods and SI Text, section 1). The appropriate nondimensional parameter for fluid-dynamical simulation of the diabatic heating experienced by the cumulus clouds is the heat-release number (10),

β ¼ g Q G ρ 3 ; Fig. 1. (A–D) Schematic of different physical models for cumulus-cloud Cp bbUb evolution with time. Arrows inside plumes indicate the direction of mean motion relative to plume head. where β is coefficient of thermal expansion of the cloud fluid, ρ g is acceleration due to gravity, Cp and are respectively specific cipitating cumulus-cloud flows. The transience of the plume re- heat at constant pressure and density of the ambient fluid, Q is flects the fact of generally short cumulus life times [O (103–104 s) 102 off-source volumetric heating rate, and bb and Ub are length and in nature and O ( s) in the laboratory]. [Another instance velocity scales; e.g., at condensation level in the cloud or begin- where a nonstationary entrainment model has been proposed ning of heat generation in the apparatus. In the atmosphere Q is is magmatic systems (30).] Volumetric heat generated in an O(1 Wm−3) (31) and G ¼ 0.1–2 (28). The same range of values appropriate region of the plume simulates the release of latent of G can be obtained in water subjected to a heating rate of O heat above condensation level in clouds, including other contri- (4 MWm−3), which over a volume of order 250 cm3 is a manage- butions such as from radiation. The present model (Fig. 1D) thus able 1–2 kW. The heat “injection” zone (HIZ) extends over a emphasizes the inherently nonself-similar and evolutionary char- selected height range in the plume (Fig. 2 and Fig. S1), over which acter of turbulent cloud-flow dynamics, and provides a unified flow is accelerated by the enhanced buoyancy due to heating. framework to explore entrainment/detrainment across the whole Both heating “history” (i.e., temporal variation of Q) and its “pro- cloud boundary. file” (distribution in the vertical) can be varied in the apparatus, enabling generation of any model flow in Fig. 1, and management Simulated Cloud Forms and Evolution of flow evolution by manual active control. The apparatus can The canonical cloud flow studied here is basically a round turbu- also simulate the boundary-layer-topped inversion that subjects lent plume or jet. The flow apparatus (Fig. 2) built for the pur- the cloud to stratification at lower levels (LLS), and/or the trade-wind inversion which does the same at higher levels (ULS); in between, the ambient fluid (nonconducting deionized water) is neutrally stable. To demonstrate the versatility and power of the present experimental technique and flow model, we first illustrate pictorially a few of the many varieties of cumulus flows that can be created in the apparatus merely by varying flow, heating and stratification parameters (other examples can be found in ref. 32). Fig. 3 pre- sents a set of five paired images comparing laboratory-simulated cloud flows with observed natural clouds (henceforth “simulations” and “clouds” respectively; corresponding heating histories A and profiles are given in Fig. S2). Fig. 3 depicts a typical cumu- EARTH, ATMOSPHERIC, lus congestus formed when convection is vigorous and heat gen- AND PLANETARY SCIENCES eration occurs over an appreciable volume. (Cloud types are designated as in ref. 33.) In the simulation, plume growth is constrained by stratification at LLS, first spreading active fluid around this level. With injection of sufficient heat active fluid penetrates the inversion (compare Fig. 3F) and forms a “cauliflower” shaped congestus. The cumulus “tower” in Fig. 3B is a commonly seen deep convective cloud; it has a core that seems glaciated. In such clouds considerable positive buoyancy is added near cloud base (where water-vapor concentration is high due to presence of warmer air), and then again at middle levels following glaciation, with accompanying microphysical processes and precipitation that remove condensed water from the cloud Fig. 2. Photo schematic of the present apparatus. Active fluid issues (31). In the simulation, these effects are achieved by correspond- vertically upward into tank of deionized water from an orifice (O) at the ing variations in heating rate and profile over time (Fig. S2). base. Flow is ohmically heated in the HIZ which consists of a set of six netted In another example of a cumulus tower (Fig. 3C), the top is about electrodes placed across the flow. Heating rate and profile are controlled by to break away from the rest of the cloud (as discussed in refs. 34 varying supply voltage over appropriately selected electrodes through the and 35), as also seen in the corresponding simulation. heating-control panel (H-CP). A lower-level stratification (LLS) can be created z The relatively shallow cloud and the accompanying simulation at ls by introducing urea solution into the bottom of the tank. The upper- in Fig. 3D indicate weak convective motions as in cumulus med- level stratification (ULS) can be created at zus by activating a wire heater just below the free surface of the water in the tank. Temperature is measured iocris. The diffuse base and edges indicate a dissipating cloud. at three points: in the plume chamber (T c ), in the ambient fluid (T a), and In the simulation, heating is injected for a short duration to at the ULS (T us), using resistance temperature detectors (RTD). Δρls is the make the active fluid rise, and then both power and flow are density jump at the LLS. switched off (Fig. S2). This produces, in combination with the

Narasimha et al. PNAS ∣ September 27, 2011 ∣ vol. 108 ∣ no. 39 ∣ 16165 Downloaded by guest on September 30, 2021 Fig. 3. (A–F) (Rows 1 and 2) Comparison of clouds (Left) with simulations (Right). [In some pictures backgrounds of the images, especially (E) and (F), have been digitally denoised]. (Row 3) Sequence of snapshots in cumulus-cloud evolution following a Namias scenario (34). (Lower)(Left) Heating and flow history, (Right) heating profile during cumulus evolution; color code at extreme right shows increased rate of heating in the direction of the arrow. Reynolds number is defined as Re ¼ Ud∕ν, where U is orifice-exit velocity, d is orifice diameter and ν is kinematic viscosity. For other symbols see Fig. 2 caption. Note that the temperatures are averaged over the duration of the experiment. Classification: (A), (B), (C), (F): t1–t4)—cumulus congestus; (D)—cumulus mediocris (in dissipating stage); (E)—cumulus fractus (popularly known as “scud”); (F): t5)—altocumulus cumulogenitus. The natural cloud in (E) is from ref. 36 and in (B) image from NOAA Research, courtesy of Jim W. Lee, National Weather Service.

ULS, a slowly sinking transient plume whose shape (including profile) is a sequence of snapshots depicting major stages in the the saddle-like depression on the top surface) is strikingly similar evolution of a cumulus congestus into an altocumulus (culminat- to that of the counterpart cloud. Both cloud and simulation ing in the image in Fig. 3E). At t1 we see the classical cauliflower appear to be tending toward a cumulus fractus characterized by type congestus which turns into a tower at t2. Here the LLS, frayed edges. mimicking a boundary-layer-capping inversion, forms the cloud E Fig. 3 shows an example of a cloud with shreds dangling base, and the convective flow is a diabatically heated starting below the nominal cloud base, perhaps dragged down by preci- plume. After the flow to the plume chamber is turned off and pitation loading and/or evaporative cooling. In the simulation the a burst of heating applied just before t3, the transient plume thins heating history and profile are the same as in Fig. 3F: heat is down close to the LLS and detaches from it soon afterward. At added for 100 s and then switched off along with the flow. At the time of the picture (t ¼ 265 s) the top of the simulation plume is t4 there is neither active fluid nor heat generation in the HIZ, held nearly stationary by the warm ULS, and the heavier fluid and the flow collects into an isolated congestus. It then ascends near the base starts descending. The rather irregular descent is further and encounters the ULS between t4 and t5. Finally the probably due to inhomogeneities caused by convective turbulent flow spreads around zus (at t5), and ends up simulating an alto- motion, in nature (36) as in the laboratory, resulting in the frayed cumulus cumulogenitus (illustrated in ref. 33, 36). The transfor- edges of a cumulus fractus. mation seen in Fig. 3F largely follows the scenario mentioned We now illustrate simulation of an evolving cumulus-cloud by Namias (34) for vigorously growing clouds. Other simulated flow. Fig. 3F (with lower panels showing heating history and evolution histories can be found in ref. 32.

16166 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1112281108 Narasimha et al. Downloaded by guest on September 30, 2021 Dynamics of Anomalous Cumulus Entrainment stages (45, 46), namely engulfment of ambient fluid by coherent Fig. 3 demonstrates that the present flow model and apparatus structures in the flow, and drawing the engulfed fluid into can capture remarkably well many observed features of several stretched and squashed shapes that vastly increase their interface cumulus-cloud types (two genera and three species) and cloud area through a stirring action (also called “mingling”). Visualiza- evolution through three different types. We now show that tion by laser-induced fluorescence has shown (10, 28, 37) that laboratory studies of diabatic plumes offer unique insights into off-source heating disrupts coherent structures in the upper re- the long-debated entrainment anomalies of cumulus clouds, and gion of HIZ and beyond, and can therefore disable the entrain- help unravel the dynamics underlying certain distinguishing ment process at the engulfment stage itself (see also refs. 47 and features of cumulus-cloud flows. For this purpose we present a 48). Furthermore, experiments (28) in steady diabatic plumes critical analysis of long-time averaged data on diabatically heated have also revealed the presence of the protected cores of ref. 21 steady-state jets and plumes acquired using laser Doppler (10, 37) (see SI Text, sections 4 and 5 and Figs. S3 and S4). Taken together and particle imaging (29, 38) velocimetry. The steady flow is a with the demonstration of nonsimilarity, the present diabatic- limiting case of the transient-plume model, and allows us to focus plume model helps resolve major puzzles in cumulus entrainment exclusively on the effect of heating on lateral entrainment as a dynamics (16). first step in understanding the more complicated dynamics of These results from steady-flow laboratory simulations are evolving clouds that involve cloud-top entrainment as well. directly applicable to tropical deep convection, for which steady- Furthermore, it makes possible cross-validation of laboratory state numerical solutions of a fully compressible cloud-resolving results with recent computations (26) of a steady-state deep con- model (CRM) have recently been presented (26). The computa- vection model. tions are carried out for a cloud system in radiative-convective Many different definitions of entrainment rate have been equilibrium with a model for microphysics (49). A major output reported in the cloud-physics literature (8, 15, 39). The most of this work is a dilution-related variable termed “purity” (p), appropriate formulation for the present cloud-flow model is the “ ” obtained by releasing passive purity tracers at cloud base zb entrainment coefficient (15) first introduced by Taylor (40), and computing their concentration in “cloudy parcels” (taken as those with liquid-water mixing ratio >10−5 kg∕kg and updraft α ¼ð2πρ Þ−1 ∕ E bUc dm dz; velocity >1 m∕s) at any height z. A time-averaged flux-weighted ð Þ¼1 purity (pc) is then computed, with pc zb . To make connec- where m is the total vertical mass-flow rate at z, b the velocity tions with the experiments reported here, we need a surrogate width of the flow, and Uc the centerline velocity, all the quantities for liquid-water content in the natural cloud. This may be for- being long-time averages. Fig. 4 shows the vertical variation of α mulated, to a first approximation, by realizing that the latent- E measured in three different laboratories (10, 29, 38) in appa- heat release accompanying condensation into liquid water results ratus similar to that originally developed in ref. 10. Four (10, 29, in temperature differences, which are present in the laboratory 37) of the five datasets shown are in broad agreement on the α simulation by heat generation in dye-colored active fluid. The effect of heating. Over the lower HIZ E exhibits a mild increas- dye particles used for flow visualization in the laboratory can, ing trend above the cloud-base level (z ), reaches a maximum, b therefore, act as the purity tracers of ref. 26. We now introduce and then falls relatively rapidly, often virtually to zero, in the the concept of a “diabatic purity” (p ) for laboratory flows based upper HIZ and/or beyond. This variation is broadly consistent d on dye concentration. To facilitate comparison with the results in with observations in natural clouds (25, 41, 42). The fifth dataset ref. 26 we further define a flux-weighted average diabatic purity, (38) shows α rising first to a very high value in the lower HIZ, E which can be written as later falling to zero or even negative values in the middle, and Z rising once again toward the end. Although the precise reasons z −1 ð Þ¼ ð Þ∕ ð Þ¼ 1 þ ð2πρα Þ ∕ ð Þ are not known, the excessive turbulence levels found at the base pd z m zb m z EbUc dz m zb ; of HIZ in the experiments may be responsible, among other zb factors (43), for this behavior (SI Text, section 3 and Table S1). Materials and Methods ð Þ¼1 Otherwise the overall results of Fig. 4 clearly show that, with (see for the derivation), with pd zb . EARTH, ATMOSPHERIC,

α AND PLANETARY SCIENCES off-source heating, values of E depart significantly from the con- Fig. 5 compares laboratory estimates of purity with the CRM stancy suggested by similarity theory. A plausible explanation values (26). From unity at zb the diabatic purity drops rapidly in “ ” ð − Þ∕ ≅1 for such behavior stems from current understanding of the fluid the HIZ, displays a knee at z zb L , and decreases much dynamics of mixing in turbulent shear flows. In this picture mo- lecule-level mixing (44) in such flows is preceded by two other

Fig. 4. Vertical variation of measured entrainment coefficient, with uncertainty band (see SI Text, section 3), in diabatically heated steady jets and Fig. 5. Comparison of flux-weighted average purity in the laboratory plumes. L denotes vertical extent of HIZ, αEb is entrainment coefficient in experiments with that in the CRM computations (26). The error bar shows unheated flow at zb. typical uncertainty in the measurements of Venkatakrishnan (37).

Narasimha et al. PNAS ∣ September 27, 2011 ∣ vol. 108 ∣ no. 39 ∣ 16167 Downloaded by guest on September 30, 2021 more slowly further above. The extreme limits in variation of pc obtained in the CRM solutions (26) for different grid resolutions, − ¼ shown in Fig. 5, also display a similar knee around z zb 1.8 km. This length is therefore used as a surrogate for L to − SI Text, section 5 normalize z zb in these computations (see ). The close agreement of the index of entrainment-driven dilution from laboratory experiments with the CRM results, seen in Fig. 5, lends support to the present diabatic-plume model of cumulus- cloud flows. Fig. 6. Block diagram showing the proposed first-order connections be- A further point must be noted. Whereas the laboratory data tween certain major aspects of the physics and dynamics of cumulus clouds. α − ¼ on E do not extend very much beyond z zb L, the CRM solutions go all the way to the tropopause. The behavior of purity Materials and Methods – in the height range 3 9 km (above zb) seen in Fig. 5 indicates Experimental Procedure. In the beginning, the test tank is filled with deio- another cycle of higher and lower entrainment in the CRM nized water. The active fluid supplied to the plume chamber is prepared results, due to glaciation now rather than condensation as in the by adding about 6 mL of hydrochloric acid per liter of deionized water, along first cycle. Glaciation appears to start soon after condensation with a small quantity of anodizing dye (Aludin Red PVC) for coloring the flow, (see figure 8 in ref. 26), and it is for this reason that the plateau and acetone for density balance. Lower-level stratification is introduced into the tank by adding urea to deionized water in a separate tank and slowly near 1.8 km in the CRM solutions is not as marked as in the pumping the solution through each of four diffuser sectors on the floor laboratory. of the tank (Fig. S1). The flow rate is kept low to avoid disturbances and is carefully adjusted to be the same through all the sectors. Once there is Implications of Laboratory Cloud Simulations enough water in the tank, the upper-level free-surface heater is turned As an illustrative example of the far-reaching implications of on for about 10–30 min to obtain the required temperature rise (2–9°Cin the present findings, we present here the case of “homogeneous” present experiments) to effect upper-level stratification. To perform whole- vs. “inhomogeneous” mixing [as it has been called (7)] in clouds. field flow visualization, the region of interest is illuminated using LED (light This is of great significance in current microphysical studies (7, 9). emitting diode) panels and halogen lamps. Videos and photographs are captured using a Nikon D-90 DSLR camera. The values of temperature, vol- Mixing of environmental with cloudy air is called homogeneous tage, and current are recorded over the entire duration of the experiment (inhomogeneous) if the ratio of the turbulent mixing time scale (typically 5 min for one run). Using real-time data displayed by the data- τ ( mix) to a thermodynamic time scale associated with droplet logger as sensor inputs, and the flow-control valve, applied voltage and evaporation (7) is small (large). In recent airborne measurements control-panel switches as actuators, active control can be exerted manually of trade-wind cumuli (50), the mixing was found to become more to manage the flow. τ homogeneous with increasing height from cloud base (with mix p decreasing approximately from 12 s to 7 s over a height of about Estimation of Diabatic Purity ( d ). In the CRM computations (26), the flux- z p ¼ SI Text, section 6 weighted average purity of cloudy updrafts at a given altitude is c 650 m; see ). In another study (7) the mixing was _ _ ∫ AðpmcÞdA∕∫ AmcdA, where the integral is taken across the cloud area reported to be predominantly homogeneous near cloud tops in AðzÞ and m_ c is cloudy updraft mass flux (i.e., mass-flow rate per unit area); two growing clouds out of the four on which measurements were note that both pðzbÞ and pc ðzbÞ¼1 by definition. On lines similar to Romps made. Qualitatively similar behavior is observed in the present and Kuang (26), the flux-weighted average concentration of dye particles c ðzÞ¼∫ ðcm_ ÞdA∕ experiments on steady diabatic flows, in which rough estimates of (which serve as purity tracers in the laboratory) is a A c ∫ m_ dA “ ” the turbulent mixing time scale indicate that it decreases approxi- A c . To calculate cloudy mass flux in the laboratory flows we write m_ ¼ kðΔTÞm_ k “ ” mately by a factor of two (from 1.5 s to 0.7 s) with height over the c , where is an analogue of the activity operator of ref. 8, τ SI Text, ΔT (a surrogate for the liquid-water content in ref. 26) is the excess tem- extent of the HIZ (for details on the estimates of mix see section 6 perature of the diabatically heated flow over the corresponding unheated and Table S2). This is consistent with lower dilution flow, and m_ is the measured mass flux. (Note that k ¼ 1 for cloudy parcels due to the distortion [owing to axial acceleration (47, 51)] and and 0 otherwise). Because ΔT was not measured in the experiments of disruption of coherent structures (10, 48), accompanied by faster refs. 10 and 37, it is not possible to determine the activity operator k directly. mixing due to intensification of small-scale vorticity caused by the In another study (54), temperature measurements in the HIZ in a heated jet baroclinic torque (48), both resulting from off-source diabatic show that the time-averaged ΔT (and hence also the probability of finding a ΔT heating. These physical effects make conditions favorable for parcel with higher ) is higher near the core of the flow than at the edges, as the laboratory flows in question (10, 37, 54) are statistically stationary. more homogeneous mixing as we move up beyond cloud base. This implies that the action of k is to reduce the effective width of the flow. Another area where the present results can prove of value is It is thus reasonable to assume that the effect of this reduction on the terms _ _ the representation of convective clouds in weather and climate ∫ Aðcmc ÞdA and ∫ AmcdA is of the same order, and therefore caðzÞ≅ _ _ models. In certain parameterization schemes using plume models ∫ AðcmÞdA∕∫ AmdA. The average diabatic purity for the laboratory flows p ðzÞ¼c ðzÞ∕c ðz Þ (52, 53), the mass-flux profiles generated are particularly sensitive can now be defined as d a a b (choosing the value at the base ðd∕dzÞ∫ ðcm_ ÞdA≅0 to the precise variation of the environmental-inflow rate with of HIZ for normalization). Noting that A because dye c ðzÞ∕c ðz Þ¼mðz Þ∕mðzÞ height (52), and its specification so far has been more or less mean flux must be conserved, we have a a b b , where m ¼ ∫ mdA_ . Thus the diabatic purity may be estimated as pd ðzÞ¼ ad hoc. Data like those in Figs. 4 and 5 can provide a rational A mðzbÞ∕mðzÞ. Note that the diabatic purity, derived here, is best seen as a basis for more realistic specification of cloud-dilution rates. This laboratory counterpart of (and not necessarily identical to) the purity can potentially enhance the effectiveness of cumulus parameter- computed in ref. 26. However, both are dilution-related in the same way ization schemes, thereby improving skill in weather/climate pre- as detailed above and this makes the comparison in Fig. 5 in the main text dictions. meaningful. (See SI Text, section 5 for further details.) The success of the present laboratory simulations suggests that diabatic off-source heating, with its temporal and spatial ACKNOWLEDGMENTS. We thank Professor M. R. S. Rao, President of Jawaharlal Nehru Centre for Advanced Scientific Research for a grant variations, may be the missing link between cumulus microphysics toward this project, and many students in the Fluid Dynamics Lab for and macroscale dynamics. The block diagram in Fig. 6 sum- their help during the experiments. We acknowledge useful discussions marizes the emerging picture. We believe simulations of the type with Dr. S. R. Rajagopalan and Dr. L. Venkatakrishnan of National Aerospace presented here offer a powerful tool that can complement the Laboratories, Bangalore and with Prof. O. N. Ramesh of Deparment of Aerospace Engineering, Indian Institute of Science, Bangalore. R.N. thanks current emphasis on the effect of small-scale turbulence on cloud the Centre for Atmospheric and Oceanic Sciences, IISc for their continued physics. hospitality.

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