Why Are There Large Spaces of Blue Sky Between Cumulus Clouds

Cumulus Clouds

A cumulus cloud is clearly the product of interactions between the gravity wave field and convective thermals, which generally have their origins in the atmospheric boundary layer.

From: International Geophysics , 2011

Storm and Cloud Dynamics

William R. Cotton , ... Susan C. van den Heever , in International Geophysics, 2011

7.1 Introduction

Cumulus clouds take on a variety of forms and sizes ranging from non-precipitating fair-weather cumuli to heavily precipitating thunderstorms. In this chapter we shall discuss the dynamic characteristics of cumuli, ranging from boundary layer cumuli to towering cumuli or cumulus congestus. Stull (1985) proposed a classification of fair-weather cumulus clouds according to their interaction with the atmospheric boundary layer. He considered three categories: forced, active, and passive clouds. Figure 7.1 illustrates the differences among the three cloud categories. Forced cumulus clouds form at the tops of boundary layer thermals that overshoot into the stable layer that caps the ABL. The thermals rise above the lifting condensation level but because they are unable to rise above the level of free convection (LFC), they remain negatively buoyant during overshoot. Active fair-weather cumulus clouds ascend above the LFC and therefore become positively buoyant. As a consequence of gaining positive buoyancy, they ascend to greater heights than forced cumuli, and develop circulations that depart from those characteristic of dry ABL thermals. Passive clouds are the decaying remnants of formerly active clouds. They can be readily identified by the absence of a flat base. Their importance is mainly due to the fact that decaying clouds may account for a significant fraction of the total cloud coverage (Albrecht, 1981). This is especially true on those days in which the free atmosphere is humid and cloud evaporation is slow. Thus, passive clouds can significantly affect the amount of radiative heating/cooling in the ABL. Over land, passive clouds mainly affect the ABL by shading the ground and thereby reducing surface heating. We begin this chapter by examining boundary layer or fair-weather cumuli as an ensemble of cloud elements that can be thought of as an extension of the cloud-free boundary layer. We then examine the organization of cumulus clouds. Finally, we focus on the properties of individual cumuli by examining the processes of entrainment in cumuli and the initiation and maintenance of convective-scale updrafts and downdrafts, and the interaction of clouds.

FIGURE 7.1. Schematic of the relationship of cumulus clouds to various fair-weather mixed-layer (ML) characteristics. The lightly shaded region denotes ML air, the black region denotes free-atmosphere air, and the white regions denote clouds. The horizontal average ML depth is indicated by $Z_i$ , while $Z_i$ is used for the local ML top. The dotted line shows the local lifting condensation level (LCL) for air measured at $Z_i$ ; the short-dash line shows the local LCL for air measured in the surface layer; the long-dash line shows the local level of free convection (LFC) for air measured in the surface layer. Cloud classes are labeled above their respective sketches.

From Stull (1985)

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CLOUDS | Classification

A.L. Rangno , in Encyclopedia of Atmospheric Sciences, 2003

Convective Clouds

Cumulus and cumulonimbus clouds (Figures 9 and 10 , respectively) are convective clouds brought about when the temperature decreases rather rapidly with increasing height. Differential heating and converging air currents in this circumstance can therefore send plumes of warmer air skyward with relative ease. Convective clouds are limited in coverage compared with stratiform clouds and, except for the anvil portions of cumulonimbus clouds, rarely cover the entire sky or do so only for short periods. This coverage characteristic differentiates, for example, stratocumulus clouds, with their linked cloud bases covering large portions of the sky, and similar-sized cumulus clouds that by definition must be relatively scattered into isolated clouds or small clusters with large sky openings.

Cumulus clouds have a size spectrum of their own that ranges from cumulus fractus, those first cloud shreds that appear at the top of the convective boundary layer, to congestus size (more than about 2   km deep). Between these sizes are cumulus humilis and cumulus mediocris clouds, which range between about 1 and 2   km in depth, respectively. The tops of these larger clouds are marked by sprouting portions called turrets that represent the growing and usually warmer parts of the cloud. Individual turrets are generally one to a few kilometers wide, though in strong storms individual turrets may coalesce into groups of many turrets to form a large, tightly packed, and hard-appearing cauliflower mass that roils upward with little turret differentiation.

Prior to reaching the cumulonimbus stage, cumulus clouds are therefore composed of droplets and contain very few if any precipitation particles. Precipitation, however, usually begins to develop in cumulus congestus clouds if they are more than about 3   km thick over land and about 2   km thick over the oceans. The precipitation that falls may be due to collisions, with coalescence of the larger cloud drops in the upper portions of the cloud (particularly when the cloud base temperature is above 5–10°C), or it may be due to the formation of ice particles in clouds with cooler bases. However, in the wintertime, even small cumulus clouds with tops colder than about −10 to −15°C can produce virga, snow flurries, or even accumulating amounts of snow. These kinds of small, cold, and precipitating cumulus clouds are found in wintertime in such locations as the Great Lakes of the United States, off the east coasts of the continents, or over high mountains.

If significant precipitation begins to develop in deep cumulus clouds, they quickly take on the visual attributes of cumulonimbus clouds (Figure 10); a strong precipitation shaft is seen below cloud base with a cloud top that is fibrous, fraying, or wispy. The visual transition to a softer, fibrous appearance in the upper portion of cumulus clouds is due to the lowering of the concentrations of the particles from hundreds of thousands per liter of relatively small cloud droplets (<50   μm diameter), to only tens to hundreds per liter of much larger (millimeter-sized) precipitation-sized particles (rain drops or ice particles). These larger particles tend to fall in filaments and help produce a striated appearance.

In the period while this transformation is taking place and the fibrosity is just becoming visually apparent in the upper portions of a cumulus congestus cloud as this particle spectrum change is underway, the cloud is entering a short-lived period of its life cycle when it is referred to as a cumulonimbus calvus ('bald') cloud (Figure 13). At this same time, a concentrated precipitation shaft may be just emerging below cloud base. When the fibrosity of the upper portion of the cloud is fully apparent, the cumulonimbus cloud has transitioned to a cumulonimbus capillatus ('hairy') in which most or all of its upper portion consists of ice crystals and snowflakes. In the tropics, this visual change also occurs but can be due solely to drizzle and raindrops in smaller cumulonimbus clouds. If a pronounced flattening of the top develops into a spreading anvil, then the cloud has achieved the status of a cumulonimbus capillatus incus ('anvil').

Figure 13. Cumulonimbus calvus.

Cumulonimbus capillatus clouds span a wide range of depths, from miniature versions only about 2   km deep in polar air masses over the oceans, to as much as 20   km in the most severe thunderstorms in equatorial regions, the plains of eastern China, and the plains and south-east regions of the United States. Hail or graupel (soft hail) are usually found, if not at the ground then aloft, in virtually all cumulonimbus clouds. Updrafts may reach tens of meters per second in cumulus and cumulonimbus clouds, particularly in warm air masses. These updrafts lead to large amounts of condensation and liquid water content. Depending on how warm cloud base is, the middle and upper building portions of deep cumulus clouds might contain 1–5   grams per cubic meter of condensed water in the form of droplets and rain drops. When 'supercooled', such liquid water concentrations are sufficient to cause a buildup of about 1   cm or more of ice on an aircraft frame for every minute in cloud and thus pose a great hazard for aircraft. Cumulonimbus are the only clouds, by definition, that produce lightning. That is, if lightning is observed, the cloud type producing it is automatically designated a cumulonimbus cloud.

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CLOUDS AND FOG | Classification of Clouds

A.L. Rangno (Retiree) , in Encyclopedia of Atmospheric Sciences (Second Edition), 2015

Convective Clouds

Cumulus and cumulonimbus clouds (Figures 16–25, respectively) illustrate convective clouds, those clouds brought about when the temperature decreases rather rapidly with increasing height above the ground. Differential heating and converging air currents in this vertical temperature structure can therefore send plumes of warmer air skyward with relative ease since those plumes will likely be warmer than the air around them.

Convective clouds are limited in coverage compared with stratiform clouds and, except for the anvil portions of cumulonimbus clouds, rarely cover the entire sky or do so only for short periods. This coverage characteristic differentiates cumulus clouds, for example, from stratocumulus clouds because the latter have linked cloud bases covering large portions of the sky. Similar-sized cumulus clouds must, by definition be relatively scattered into isolated clouds or small clusters with large sky openings.

Cumulus clouds are roughly divided into species by their depths. For example, cumulus fractus, those first cloud shreds that appear at the top of the convective boundary layer, may be less than 100   m thick. Cumulus humilis (Figure 16), the next larger size, should not be more than 1   km thick and looks more like a fat pancake than a heaped up cloud. Figure 17 shows that in very cold situations, that even cumulus humilis clouds can form ice. Cumulus mediocris clouds (Figure 18) show clouds that are beginning to be humped up and resemble the profiles presented by mountain ranges. They are around 1–2   km thick. The largest cumulus species is cumulus congestus (Figure 19), always more than about 2   km deep to several kilometers deep and generally much taller than they are wide.

The tops of these larger cumulus clouds, mediocris and congestus, are marked by sprouting subelements referred to as turrets that appear as noticeable protuberances at the top. Turrets are also crenelated on their surface with dozens of lesser, tuft-like 'units' perhaps tens of meters wide. Turrets are generally one to a few kilometers wide. However, in severe thunderstorms, individual turrets may coalesce into groups of many turrets to form a large, tightly packed, and hard-appearing cauliflower mass that roils upward with little turret differentiation.

Cumulus clouds are, with rare exceptions discussed below, composed solely of droplets. They have the highest liquid water concentrations of any clouds in their upper portions where the moist air has been lifted the highest. To be a purely cumulus cloud, very few precipitation-sized particles are in them, though they may be imminent. There is no definite rainshaft, an appendage requiring the use of the modifier, 'nimbus,' Latin for rain.

The development of extensive precipitation in cumulus clouds is one in which a cumulus congestus is also becoming a cumulonimbus cloud and leaving the cumulus category. The depth of this transition is different for different aerosol regimes. In clean conditions, cumulus congestus can migrate to a cumulonimbus having a pronounced rainshaft when they reach depths of only 1.5–3   km thick, such as over the oceans. However, in polluted situations, the depth must be much greater, about 3   km thick over land. The precipitation that falls from cumulonimbus clouds can be either due to collisions with coalescence of cloud drops to form raindrops (a process termed the 'warm rain process') or it may be due to the formation of ice particles which then collect water through riming or through the aggregation of many ice crystals into snowflakes that melt on the way down. In the cases where the warm rain process is the sole producer of raindrops, the cumulonimbus clouds are necessarily shallower than those requiring an ice process for a strong rainshaft since their tops will be only around or below the freezing level altitude.

Often times in maritime locations and also for clouds in continental locales with warm bases (above about 10   °C), both processes, the warm rain and the ice process, are active.

In wintertime, even small to moderate cumulus clouds with tops colder than about −10 to −15   °C can produce virga, snow flurries, or even accumulating amounts of snow (Figure 17). These kinds of small, cold-based, and precipitating cumulus clouds are found in wintertime in such locations as the Great Lakes of the United States, off the east coasts of the continents, over high mountains or deserts regions.

When significant precipitation develops in cumulus congestus clouds, the visual attributes begin to change noticeably. In the first stage of this change, often very subtle and hard to detect without a practiced eye, the cloud is called a cumulonimbus calvus ('bald,' Figure 20). Often, a strong precipitation shaft is seen below cloud base with a cloud top that has softened from a hard, crenelated appearance. In some cases, the rainshaft has not yet appeared or is just emerging, an exciting moment! The 'soft,' fibrous, fraying, or wispy transition, sometimes compared to the look of 'cotton candy,' is due to the lowering of the concentrations of the particles from 50 to hundreds of thousands per liter of small cloud droplets (<50   μm diameter), to only tens to hundreds per liter of much larger diameter particles that are fractions of a millimeter to greater than millimeter sized. These precipitation particles can be raindrops or ice particles or briefly, both. These larger particles tend to fall in filaments and often produce a striated appearance.

This process from the 'hard' to 'soft' appearance of a cloud top takes just at few minutes, typically around five or so, that is, to the point that most observers can be recognize that 'something has changed' at cloud top from the time the cloud was a congestus. If there is already a strong shaft, it is likely that you are viewing the upwind side of a cumulonimbus cloud where new turrets are forming and are going through the complete glaciation cycle and the fibrous appearance which was normally expected to see with fully developed rainshafts is hidden from view and downwind from the observer.

When the fibrousness of the upper portion of the cloud is readily apparent, the cumulonimbus cloud has transitioned from a 'calvus' to a capillatus (Latin, 'hair' – grew 'hair' after being 'bald'!). At this point, when the capillatus stage is reached, all of the upper portion of the cumulonimbus clearly consists of ice crystals and snowflakes (Figure 21). In the tropics or in warm humid air masses, this visual transformation also occurs but can be due solely to the evaporation of the smaller drops leaving the much lower concentrations of drizzle and raindrops that result in a softening of the clouds appearance (Figure 22).

Hail or graupel (small, soft hail) are usually found, if not at the ground, then aloft in virtually all cumulonimbus clouds that reach above the freezing level.

If a pronounced flattening of the top of these clouds develops into a spreading anvil, then the cloud has achieved the status of a cumulonimbus capillatus incus (incus, Latin for 'anvil,' Figure 23). With the familiar anvil, it is perhaps the most recognizable form of a cumulonimbus cloud. The flattening at top usually indicates that the updraft has reached the tropopause, and therefore, these cumulonimbus clouds are more likely than 'capillatus' versions to be severe storms. And watch out if a mound or towering dome of cloud appears above the flattened top! That dome represents an updraft that has overshot the troposphere and entered the stratosphere, the sign of an exceptionally strong updraft within that thunderstorm. So, a dome above the anvil is a very good sign of an especially severe thunderstorm, one that you would not want to drive your car under.

Updrafts may reach tens of meters per second in cumulus and cumulonimbus clouds, particularly in warm air masses. The greatest updraft speed that has been measured by an aircraft was an astounding 40   m   s⁻¹! These strong updrafts lead to large amounts of condensation and liquid water content in the upper regions of these clouds, and often at temperatures far below freezing, even to −30   °C!

Depending on how warm cloud base is, the middle and upper developing portions of deep cumulus clouds might contain 1–5   g   m⁻³ of condensed water in the form of cloud droplets and raindrops. Supercooled water concentrations of these magnitudes are sufficient to cause a buildup of ice on an airframe of about 1   cm or more of for every 1–2   min in cloud. No aircraft can fly for long with such an accumulation of ice and therefore, cumulus and cumulonimbus clouds are avoided by aircraft.

Cumulonimbus clouds are the only clouds that produce lightning. If lightning is observed, the cloud type producing, it is therefore designated as a cumulonimbus. Unlike other clouds, too, the bases of cumulonimbus clouds are marked by strong rainshafts, a feature that differentiates them from nimbostratus clouds. Therefore, when strong rainshafts are observed (Figure 24), the cloud producing, it is also assumed to be a cumulonimbus even if lightning is not observed.

Occasionally, too, large downward projecting protuberances are seen in connection with cumulonimbus clouds. These formations are called 'mammatus,' Figure 25. Contrary to popular opinion, mammatus formations may or may not be associated with a strong thunderstorm. Mammatus are also seen in such tame clouds as altostratus and cirrus.

Cumulonimbus clouds span a wide range of depths, from miniature versions only about 2   km deep in polar air masses over the oceans, ones that never produce lightning, to as much as 20   km in the most severe thunderstorms in equatorial regions, the plains of eastern China, in Brazil and Argentina, and the plains and southeast regions of the United States. However, the most lightning on earth occurs in the interior of central Africa along the Equator.

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The Science of Hydrology

D. Koutsoyiannis , A. Langousis , in Treatise on Water Science, 2011

2.02.2.4.1 Cumulus cloud systems

Cumulus clouds are formed by small thermals (upward-moving air parcels heated by contact to the warm ground) where condensation occurs and they grow to extend vertically throughout the troposphere. Their vertical extent is controlled by the depth of the unstable layer, while their horizontal extent is comparable to their vertical extent. A typical linear dimension of a cumulus cloud is 3–10  km, with updraft velocities of a few meters per second (Rogers and Yau, 1996).

Observations performed by Byers and Braham (1949; see also Weisman and Klemp, 1986) revealed that convective storms are formed by a number of cells, each one of which passes through a characteristic cycle of stages (Figure 15). The cumulus stage of a cell is characterized by an updraft throughout most of the cell. At this stage, which lasts approximately 10–20   min, the cell develops and expands vertically while the air becomes saturated and hydrometeors grow due to vapor condensation and turbulent coalescence (see Section 2.02.2.2).

Figure 15. Stages of development of convective cells. Adapted from Weisman ML and Klemp JB (1986) Characteristics of isolated convective storms. In: Ray PS (ed.) Mesoscale Meteorology and Forecasting, ch. 15, pp. 331–358. Boston, MA: American Meteorological Society.

Some ice and water particles grow large enough to fall relative to the ambient updraft and initiate a downdraft within the cell. The downdraft is initially in saturated condition, but as it moves toward the lower troposphere and mixes with sub-saturated air, evaporational cooling occurs, which introduces negative buoyancy and accelerates the downdraft. This is the start of the mature stage of the cell, which lasts for approximately 15–30   min. The air of the downdraft reaches the ground, as a cold core, and changes the surface wind pattern. This change may initiate a new thermal at a neighboring location, which might grow to a new cell. The downdraft interferes with the updraft at the lower levels of the cloud and finally cuts off the updraft from its source region. At this point, the cell enters its dissipating stage. At this stage, which lasts for about 30   min, the updraft decays and consequently, the precipitation source is eliminated.

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Storm and Cloud Dynamics

William R. Cotton , ... Susan C. van den Heever , in International Geophysics, 2011

1.3.3 Cumulus (Humilis and Mediocris) Clouds

Cumulus clouds whose vertical extent may be 1500 m have a lifetime $\left(T_c\right)$ of 10-30 min, which is shorter than that for the preceding two types of clouds. If we consider an average vertical velocity of 3 m s⁻¹, the time scale for a parcel to enter the cloud base and exit the cloud top is of the order of

(1.4) $T_P=1500m/3m{s}^{-1}=500s\simeq 10\min \text{.}$

The liquid-water content of small cumuli rarely exceeds 1.0 g m⁻³ and is typically approximately 0.3 g m⁻³. Thus, for such short time scales and low liquid-water contents, precipitation is unlikely in all but the most maritime or cleanest airmass, wettest cumuli.

Comparing wet adiabatic cooling rates to cloud-top radiation cooling, we estimate

(1.5) $C{R}_{\gamma }\simeq (0.5{}^{\circ }C/100m)\times 3m{s}^{-1}=1.5\times 10^{-2\circ }C{s}^{-1}\simeq 50{}^{\circ }C{h}^{-1}\text{,}$

which is considerably greater than the cloud-top radiation cooling rates for clouds of such liquid-water contents $(C{R}_{\mathrm{IR}}\sim 4{}^{\circ }C{h}^{-1})$ . Thus, wet adiabatic cooling dominates radiative effects in such clouds.

The turbulence levels in small cumuli is relatively moderate, with root-mean-square (RMS) velocities ranging from 1 to 3 m s⁻¹. Thus, turbulence plays an important role in such clouds.

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Thermodynamics of Atmospheres and Oceans

In International Geophysics, 1999

8.5.1 Non-precipitating cumulus

A developing cumulus cloud is characterized by a rising thermal tower whose outline is sharply defined by protuberances with a cauliflower appearance. The protuberances continually emerge from the top of the cloud. After reaching a peak height, a tower subsides and the protuberances become less pronounced or disappear altogether. The cloud edges become tenuous and the tower evaporates completely. An individual cumulus tower goes through a life cycle of growth and decay over a period of minutes for fair weather cumulus and about an hour for towering cumulus. In the absence of precipitation, the condensation and subsequent evaporation of a cumulus cloud results in no net latent heating of the atmosphere. Cumulus clouds with diameters less than 5 km and a depth of less than 1 km are not commonly observed to precipitate.

The vertical variation in cloud liquid water content shows an increase from cloud base to within a few hundred meters of the cloud top, where it rapidly falls to zero. Figure 8.22 illustrates the vertical variation in liquid water content from cloud base to cloud top in cumulus clouds in terms of the ratio of the observed liquid water content to the adiabatic value (6.41). The ratio $w_l/w_l^{ad}$ represents the departure of the liquid water mixing ratio from the adiabatic value due primarily to the effects of entrainment. The liquid water content is seen to depart significantly from the adiabatic values within 500 m of the cloud base. The relative importance of air entrained into cumuli from the sides versus the cloud top has not been fully resolved.

Figure 8.22. Observed variation with height above the cloud base of liquid water mixing ratio, w_l as a fraction of the adiabatic value, $w_1^{a\mathrm{d}}$ in large cumulus clouds. At the cloud base, the ratio is typically near unity, but decreases rapidly with height in the cloud due primarily to entrainment.

(After Ludlam, 1980.) Copyright © 1980

Figure 8.23 shows observations of horizontal variability associated with cumulus clouds. Extreme variations in the vertical velocity are seen, from updrafts of about 6 m s⁻¹ to downdrafts of more than 4 m s⁻¹ in less than 50 m across the cloud. Upon entering the cloud, the liquid water content jumps from zero to substantial values. Within a cloud element, the liquid water content fluctuates slightly in response to vertical velocity fluctuations while maintaining high values on average.

Figure 8.23. Liquid water concentration, w_l and vertical air speeds, u_z, obtained during horizontal traverses of cumulus clouds in aircraft. The water concentration measurements were taken near 1.25 km above the cloud base and 250 m from the cloud top. Vertical air speed measurements were obtained at 1 km above the cloud base.

(Adapted from Ludlam, 1980.) Copyright © 1980

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Storm and Cloud Dynamics

William R. Cotton , ... Susan C. van den Heever , in International Geophysics, 2011

8.8.2 Autopropagation by Gravity Waves

We have seen that as cumulus clouds develop buoyancy (both positive and negative), gravity waves are excited, which tend to neutralize the buoyancy gradients ( Bretherton and Smolarkiewicz, 1989). To a large extent the depth of the layer in which the wave is traveling determines the phase speed of the gravity wave. Thus Eq. (8.10) gives us:

(8.10) $C=\frac{\mathrm{NH}}{\pi (1/2+n)}\text{,}n=0,1,2\text{,}$

where $N$ is the Brunt Väisälä, $H$ is the depth of the layer, and $n$ is the mode or vertical wavenumber.

The Brunt Väisälä frequency is given by:

(8.11) $N^2=\frac{-g}{{\rho }_o}\frac{\partial {\rho }_o}{\partial z}\text{.}$

Likewise the amplitude of the wave is proportional to the heating rate and inversely proportional to $N^2$ . Now suppose that an idealized heating profile for a growing cumulonimbi resembles the profile shown in Fig. 8.28, labeled $n=1$ for a deep troposphere heating mode. This mode produces fast-moving subsidence warming at large distances from the storm as illustrated in Fig. 8.29. Mapes (1993) noted this wave is not an ordinary wave, in the sense it does not have periodic structure in space and time. Instead he argues it is analogous to a tidal bore in water which propagates at the speed of an internal wave while irrevocably changing the depth of the water as it passes. He thus refers to these waves as buoyancy bores.

FIGURE 8.28. Vertical distribution of the thermal forcing for $n=1$ and $n=2$ and their sum. $Q_0$ is the same magnitude for each mode, positive for $n=1$ , negative for $n=2$ .

From Nicholls et al. (1991)

FIGURE 8.29. Rigid-lid solution for the $n=1$ mode. $Q_{mp}=2.0J{\mathrm{kg}}^{-1}{s}^{-1}$ , $a=10\mathrm{km}$ , $N=0.01s^{-1}$ and $t=2h$ . Shows vertical velocity. The contour interval is 6 cm s⁻¹.

From Nicholls et al. (1991)

Now suppose that the cumulonimbus has evolved into its mature phase, or an MCS has developed where low-level rain evaporation and melting of hail produces low level cooling. Likewise an anvil forms which in the case of an MCS can transform into a deep stratiform-anvil cloud with latent heating due to freezing and ice-deposition through a deep layer in the upper troposphere. The resultant idealized heating profile for this system can be represented by the $n=2$ mode and the combined effects $n^1+n^2$ are illustrated in the right-hand panel of Fig. 8.28. As shown in Fig. 8.30, initially this heating profile results in sinking motion at low levels and ascent aloft, but it reverts to a propagating wave with subsidence aloft and ascent at low levels. This ascent at low-levels with corresponding low-level convergence represents what Mapes (1993) calls buoyancy bores that favor the clustering of convection. He hypothesizes that these buoyancy bores are the mechanism for what he calls "gregarious convection" leading to the formation of "superclusters."

FIGURE 8.30. Two "buoyancy rolls." Schematic of the buoyancy bores, horizontal winds, and horizontal displacements of material lines at a time $r$ , after the two-mode heat source (3) acted near $x=0$ from time 0 until time $r_2\&lt;r/2$ . The $\ell =1$ "buoyancy rolls" (bounded on each end by $\ell =1$ buoyancy bores) has completely outrun the $\ell =2$ buoyancy rolls.

From Mapes (1993)

The wave-CISK models mentioned earlier represent a class of linear wave models in which convection is phase-locked to the convergence induced by a gravity wave. In the regions of convergence, a heating profile similar to that shown in Fig. 8.28 is imposed. The imposed heating then reinforces the gravity wave modes which then continue to propagate as a convectively-reinforced gravity wave. The problem is that numerical modeling studies of convective systems have shown that convection can excite many different scales and amplitudes of gravity waves, few of which will necessarily phase-lock with convection (Tripoli and Cotton, 1989a,b; Schmidt and Cotton, 1990). Thus the coupling of gravity waves and convection can only occur under very specific conditions.

The problem is that without phase-locking, gravity waves propagate energy vertically, and without a mechanism to reinforce the wave or reflect the wave, a wave will rapidly lose amplitude before traveling very far (Lindzen and Tung, 1976). It can be shown that reflection of gravity waves or wave trapping can occur when $l^2$ is less than $k^2$ , where $l^2$ is the Scorer parameter given by

(8.12) $l^2=\frac{N^2}{{(U_0-c)}^2}-\frac{{\partial }^2{U}_0/\partial z^2}{(U_0-c)}\text{,}$

$k^2$ is the horizontal wave number, $U_0$ is the ambient wind speed, and $c$ is the gravity wave speed. Wave trapping is likely to occur if $N^2$ is small or negative (low stability), ( $U_0-c$ ) is large (strong shear) or ${\partial }^2{U}_0/\partial z^2$ is large (a sharp jet).

There are several examples of where wave ducting can reinforce convective systems. Tripoli and Cotton (1989a,b) showed in their numerical simulations that radiative cooling at the top of a stratiform anvil layer of an MCS can lead to a layer of low stability which can serve to trap wave energy. This trapping layer can thus enhance low-level convergence and provide a mechanism for propagation of an MCS. Schmidt and Cotton (1990) simulated a squall line that was able to propagate over a stable layer such as occurs at night time over the plains of the US. The presence of such a nocturnal stable layer is not favorable for thunderstorm and squall line propagation by cold-pools or the RKW theory. Nonetheless, such nocturnal thunderstorm complexes are quite common over the High Plains of the US. Schmidt and Cotton (1990) showed that the presence of a low-level stable layer, with an overlaying layer of weak stability (sufficient to trap wave energy and support deep convection) and an upper tropospheric stable layer with both low-level shear and deep tropospheric shear, provided an ideal environment for sustaining a squall line by gravity wave propagation.

The debate about whether thunderstorms and MCSs (squall lines in particular) propagate primarily by gust front/cold-pool dynamics or gravity waves began over 60 years ago (Hamilton and Archbold, 1945; Tepper, 1950; Newton, 1950) and is sure to continue for some time to come. We will return to this discussion more when we focus on MCSs and Squall lines in Chapter 9.

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On Fire at Ten

David A. Randall , ... David O'C. Starr , in Advances in Geophysics, 1996

6.3 Interactions between Cumulus and Stratocumulus Clouds

On a few occasions during FIRE 87, cumulus clouds were found to penetrate the stratocumulus base. During ASTEX this was an extremely frequent occurrence and has enabled a study of the interaction of cumulus clouds with stratocumulus layers. The dynamic processes associated with cumulus clouds and stratocumulus are quite different and thus experience different entrainment and mixing processes. In regions where the two cloud types interact, this can have a variety of effects. Figure 36 shows a schematic diagram of the interaction.

Fig. 36. Schematic diagram of the interaction between cumulus and stratocumulus.

As mentioned previously, the cumulus clouds feed on the rich moisture supply in the SML and locally recouple the SML to the cloud layer. This has been observed to significantly thicken the stratocumulus layer and help maintain the layer for much longer than would be expected if it were permanently decoupled from the sea surface. It also modifies the thermodynamic structure of the boundary layer. This can be clearly seen in the mixing diagram of equivalent potential temperature (q _E) and total water content (q _r) shown in Fig. 37. This is a composite of several runs at different heights in a vertical stack. The dots indicate measurements in clear air, whereas the other symbols represent points in cloudy air at different heights. Area A in the diagram indicates the SML (high q _E and q _r); area B, the subcloud layer (relatively low q _E); area C, the cloud or inversion layer; and area D, the free tropospheric air (low q _r but in this case unusually high q _E). The diagram shows that mixing is occurring between these areas in the boundary layer and above. Area G shows the slow entrainment of dry, free tropospheric air. This are has been somewhat overemphasized as it was sampled during a porpoise run at cloud top where the aircraft was continually dipping in and out of the stratocumulus top and into the free tropospheric air. However, of more importance are areas E and F. Here the effects of the cumulus clouds can be seen. In area E individual cumulus clouds are being sampled as they grow from the top of the SML and mix with the subcloud-layer-air. In area F more active cumulus clouds are seen to modify the stratocumulus layer itself as their effects mix out into the layer. Here the total water content and q _E are being increased in the cloud layer (i.e., producing a stable layer) and are effectively decoupling it from the subcloud layer and presumably reducing the mixing between the two. The overall effect of this process in this case is to thicken the stratocumulus layer and increase its liquid water path and thereby increase cloud reflectivity.

Fig. 37. A mixing diagram of total water content and equivalent potential temperature for eight straight and level runs in a vertical stack during a flight on June 19, 1992 during ASTEX.

Perhaps the most significant effect of the different dynamic processes associated with cumulus clouds and stratocumulus is on the shape of the droplet size spectra in the different cloud types (Martin et al., 1994). In the relatively narrow and feeble cumulus clouds, mixing from the environment penetrates to the cloud's core and significantly modifies the droplet-size spectra; thus, the typical shapes of the cumulus and stratocumulus droplet-size spectra will differ. When the cumulus cloud penetrates the base of the stratocumulus, the two droplet-size spectra will start to mix and interact. The effects on the stratocumulus are dependent on the initial thickness of the stratocumulus. In general, the liquid water content is increased as the cumulus clouds are much deeper than the stratocumulus. Also, the droplet concentration is increased as initially the vertical velocity at the base of the cumulus cloud is higher than at the base of the stratocumulus; therefore, more CCN are activated into cloud drops because of the slightly higher maximum supersaturation. If the stratocumulus is initially very thin, the mean droplet size will be very small; therefore, the penetration of the cumulus cloud has the potential to increase the mean droplet size in the stratocumulus. However, if the layer is initially thick with relatively large droplets, the interaction with cumulus clouds will most likely result in a decrease in the mean droplet size. From the perspective of the radiative transfer characteristics of the stratocumulus layer, the change in the liquid water path dominates the interaction, with the resultant effect that the stratocumulus layer's reflectivity is increased.

During ASTEX the cumulus clouds were observed to form in clusters that occasionally had lifetimes of several hours, and it was frequently noted that drizzle accompanied the penetration of these clusters into the stratocumulus base. The cumulus clouds on their own were not deep enough (the cloud-top temperature was always above freezing) to produce precipitation, and generally the stratocumulus was too thin to produce drizzle. Thus the interaction between the cumulus clouds and the stratocumulus was in some way initiating the drizzle formation. This could be happening in several ways. The mixing of two cloud parcels of air with different droplet-size spectra will result in at least a broadening of the droplet spectra or perhaps even a bimodal spectrum. This has the potential, if the droplets become large enough, to increase the probability of coalescence, as this will increase the differential fall velocities (Hocking and Jonas, 1970; Jonas, 1972). Also, the cumulus clouds will introduce slightly higher turbulence levels in the stratocumulus layer. This is likely to help increase the collision efficiency of droplets less than 30 μm in size (de Almeida, 1976, 1979) and will also enable some of the larger droplets to remain in the cloud for a sufficient length of time that drizzle droplets can grow by stochastic coalescence (Mason, 1952; Nicholls, 1987). The cumulus clouds also increase the cloud thickness, thus providing a greater depth of cloud through which the larger drops can fall.

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HAIL AND HAILSTORMS

C. Knight , N. Knight , in Encyclopedia of Atmospheric Sciences, 2003

The Updraft and its Consequences

Humid air rising in the cores of cumulus clouds cools as it rises. The cooling causes the condensation and growth of water droplets to form the cloud, and the droplets supercool when the temperature falls below the freezing point. These water droplets are very small, and rise in the updraft almost as fast as the air rises, typically several tens of meters per second in hailstorms, because their terminal fall speeds are less than 10  cm   s⁻¹. An ice particle in such an updraft that is big enough to have a higher fall speed collides with and collects supercooled droplets, which freeze upon impact and stick to it. This is the basic mechanism of hailstone growth, and the initiating particle may be a snow crystal or snowflake or a frozen water drop. The other main role of the updraft in hail formation is to be strong enough and long-lasting enough to hold the hailstones aloft, within supercooled cloud above the freezing level, long enough for them to grow to their final sizes. If they are to reach the ground as hail, they must be big enough not to melt on the way down.

Terminal velocities of hailstones are described by

[1] $V_{\text{T}}=\sqrt{\frac{4g{\rho }_{i}D}{3C_{\text{D}}{\rho }_a}}$

In eqn [1], where C _D is the drag coefficient, a dimensionless quantity that expresses how the drag force (the air resistance) relates to the velocity and the fluid properties. The densities of ice and air are indicated by ρ; g is the acceleration due to gravity; and D is the diameter of the hailstone. Numerical values are plotted in Figure 1 for different values of C _D and, with C _D  =   0.55, for both sea level and 500   hPa pressure. A pressure of 500   hPa corresponds very roughly to −10°C and 6   km above sea level, with considerable variability depending upon local conditions. The large range of values for C _D comes about because of the highly variable shapes of hailstones, which influence fall speed considerably. Hailstone diameter is usually defined as the diameter of a sphere of equivalent mass. A hailstone growing within an updraft may ascend or descend depending upon whether its terminal fall speed is less or greater than the updraft speed.

Figure 1. Terminal fall velocities of hailstones plotted against diameter, for the drag coefficients (C _D) indicated, calculated for a pressure of 500   hPa (about 6   km above sea level) and a hailstone density of 0.9   g   cm⁻³, except where otherwise indicated. (From Knight CA and Knight NC (2001). In: Severe Convective Storms. Boston: American Meteorological Society, by permission of AMS.)

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Hail and Hailstorms☆

C. Knight , ... Katerina Skripnikova , in Reference Module in Earth Systems and Environmental Sciences, 2019

The Updraft and Its Consequences

Humid air rising in the cores of cumulus clouds cools as it rises. The cooling causes the condensation and growth of water droplets, forming visible cloud. The droplets supercool when the temperature falls below the freezing point. These water droplets are very small, and rise in the updraft almost as fast as the air rises, typically several 10s of meters per second in hailstorms, because their terminal fall speeds are <  10   cm   s^{−   1}. An ice particle big enough to have a higher terminal fall speed, within such an updraft, collides with and collects the supercooled droplets, which freeze upon impact and stick to it. This accretion is the basic mechanism of hailstone growth. The initiating particle may be a snow crystal, a snowflake, or a frozen water drop. The other main role of the updraft in hail formation is to be strong enough and long lasting enough to hold the hailstones aloft, within supercooled cloud above the freezing level, long enough to grow to their final sizes. If they are to reach the ground as hail, they must then be big enough not to melt on the way down. Terminal velocities of hailstones are described by

(1) $V_T={\left\{\left(4g{\rho }_{\mathrm{i}}D/3C_D{\rho }_a\right)\right\}}^{1/2}$

where C _D is the drag coefficient, a dimensionless quantity that expresses how the drag force (the air resistance) relates to the velocity and the fluid properties. The densities of ice and air are indicated by r, g is the acceleration due to gravity, and D is the diameter of the hailstone. Numerical values are plotted in Fig. 1, for different values of C _D and, with C _D   =   0.55, for both sea level and 500   mb pressure. Pressure of 500   mb corresponds very roughly to −   10°C and 6   km above sea level, with considerable variability depending upon local conditions. The large range of values for C _D comes about because of the variability of hailstone shape, which influences fall speed considerably. Hailstone "diameter" is often used, deceptively, to refer to the longest dimension. In the context of Fig. 1, the more appropriate meaning is the equivalent spherical diameter. A hailstone growing within an updraft may be ascending or descending, depending upon whether its terminal fall speed is less or greater than the updraft velocity.

Fig. 1. Terminal fall velocities of spherical hailstones plotted against diameter, for the drag coefficients (C_D ) indicated, calculated for a pressure of 500   mb (50   kPa, about 6   km above sea level) and a hailstone density of 0.9   g   cm^{− 3}, except where otherwise indicated.

From Knight, C. A., Knight, N. C., (2001). Hailstorms. In: Doswell, C. A., III. (ed.) Severe convective storms. American Meteorological Society, Boston, pp. 223–254, by permission of AMS.

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