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an anvil subsides, then the air within the anvil warms at the moist-adiabatic
rate, while the air being pushed down under the anvil warms at the faster dry-
adiabatic rate. The result of these two differing rates of warming is that the
lapse rate at the base of the anvil steepens, perhaps to the point of initiating
convection. (b) When ice crystals sublimate or raindrops evaporate as they fall
from the anvil into unsaturated air below, the air cools and may become
negatively buoyant, leading to upside-down convection. (c) When ice crystals fall
out of an anvil and pass below the melting layer, latent heat is released and the
lapse rate is steepened, perhaps to the point of initiating upside-down convection.
(d) When there are local variations in the mass of hydrometeors, the more massive
ones fall more quickly and air motion around the leading edge of the falling
hydrometeors descends more rapidly, creating segments of upward-flowing air to
compensate for the air being moved out of the way (imagine Figure 2.10 upside
down). (e) When ice crystals in the anvil flow over unsaturated air below, there is
mixing at the interface between the anvil base and the clear air below. Kerry
Emanuel in the early 1980s showed that when all the anvil material evaporates (or
sublimates), air at its base and underneath may become negatively buoyant. This
type of instability is termed ''cloud-base detrainment instability'' (CDI), which is
analogous to ''cloud-top detrainment instability'', which can occur at the top of
clouds when the air above the clouds is cool and dry. If the relative humidity of
the air underneath the anvil is too high, evaporative cooling (sublimation cooling)
is too slow to counteract adiabatic warming due to subsidence and, if the relative
humidity of the air underneath the anvil is too dry, evaporative cooling (sublima-
tion cooling) is too fast and the lapse rate becomes stable. A necessary condition
for CDI is that the liquid water or ice static energy 2 (C p T þg z þ Lr l = i ) of the dry
subcloud air is greater than that of the cloud air above (in the anvil). The initial
source of mixing might be Kelvin-Helmholtz instability, which occurs when the
Richardson number (Ri) is small. The Ri is small when vertical shear is large, as it
should be under the base of an expanding anvil and when the lapse rate is low.
(f ) Radiative cooling at cloud top (due to longwave radiation loss to space)
may result in a steep lapse rate within the top of the anvil, leading to convective
eddies, some of which reach downward through the anvil, reaching its base.
Radiative heating at cloud base (due to upwelling longwave radiation from the
ground that cannot pass upward through the anvil) may lead to a steep lapse rate
within the bottom portion of the anvil. (g) Double-diffusive convection (due to
''biconstituent diffusion''), which has been used to explain some convection in salt
water and unsuccessfully to forcing along the dryline, might be used to explain
mamma formation: the cloud particles and the air are the two constituents, the
former contributing to negative buoyancy and the latter to either positive or
negative buoyancy. The diffusion rate of heat is greater for cloud particles than
for air. Kathy Kanak and Jerry Straka at OU (University of Oklahoma) found in
recent idealized, high-resolution, numerical simulation experiments that CDI is a
necessary but not
sucient condition for mammatus
formation, and that
2 For liquid water, r l is used; for ice, r i is used.
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