Download PPT

Rain rate
• If the drop size distribution is n(D), and fall speeds v(D), net vertical flux of drops (m-2 s-1)

   (w  v(D))n(D)dD
0
• The “threshold diameter” has v(Dth
) = w. Smaller drops move up, larger ones move down.

rain
• The larger that w is, the larger Dth must be  Large rain rates tend to have large drops
• The rain rate at the surface is this flux computed at the ground (w=0)
• Mass flux [kg m-2 s-1] of rain hitting the ground:
Size distributions of rain drops
Modified gamma distribution
Alternative form of gamma distribution:
Setting b=0 yields an exponential –
with n0 = 8×103 m-3 mm-1 and
Λ = 41 R-0.21 (R in mm h-1), this is
the Marshall-Palmer distribution
 only captures large tail
Evolution of drop size distribution
(starting with Marshall-Palmer)
1
2
Largest break up
3
Collection and
disruptions oscillate, but
after 30 min get trimodal
Smallest get collected
quickly – but some
replenished as smaller
“grow in” by condensation
And fragments
end up here
Important to note that very large
drops not allowed to survive by
physics – 8 mm diam sometimes
observed, but GCCN origin invoked
Reminder: Warm cloud
(supersaturation via adiabatic expansion)
What are
these?
Exchange of energy
with environment by
virtue of a T difference
Diabatic condensation: entrainment effects
• An air parcel may rise adiabatically in the core of a
cloud, but turbulent motions eventually mix in
dry environmental air
• This mixing smooths out gradients  dry air
moistens and cloudy air dries
• Compare the time scales:
τevap << τmixing
• This means that the drops respond quickly
to the drier air  some drops evaporate until the
air is resaturated (according to the new conditions)
• Overall, retain the original distribution but
ND has decreased
• BUT: now ND decreased 
condensational sink is REDUCED!  supersaturation RISES
faster than in neighboring cloud elements
growth rates increase  those surviving drops get
larger than neighbors who didn’t see an entrainment event
• When the processed air gets mixed in with those
neighboring drops later, the final drop distribution
will be broader
Diabatic condensation: radiative effects
• Consider droplets near the top of the cloud:
if they “see” a cooler atmosphere above them,
they can radiate away some of their energy
 their temperature DROPS
• So the vapor pressure at the drop surface is
DECREASED  drops grow faster
• Interestingly, the radiative cooling is proportional to
the cross-sectional area of the droplet  so large drops cool more
• Harrington et al. (2000) showed that in a marine Scu environment, when drops compete for a limited
supply of water vapor, the larger drops grow so rapidly via this enhancement that drops with
diameters < 20 µm evaporate  bimodal drop size spectrum!
• Only effective in clouds where drops can reside near cloud top for 12 min or more
• Cumulus clouds with vigorous overturning “expose” drops to space for too short a time
Hartman and Harrington, 2005
Arctic stratus cloud example
Drops smaller than
~10 µm are
prevented from
growing!
With radiative
effects
Without
Autoconversion
• “Autoconversion” is the process of collision-coalescence that leads to the formation of
new small drizzle drops
• In models, we generally cannot represent this process explicitly
• The “drizzle drop threshold” is generally taken to be r = 20 µm (other choices exist)
• Parameterizations express the autoconversion rate in terms of drop size distribution
moments, such as liquid water content (LWC) [Kessler, 1969], cloud droplet number
concentration, or spectral dispersion
• The computed autoconversion rate is used to transfer water mass from “cloud drops” into
“drizzle drops” (sets time scale) in order to initiate precipitation
• When autoconversion is active, an average collision frequency is assumed for all cloud
droplets, resulting in an autoconversion rate that scales with LWC7/3
On the representation of droplet coalescence and autoconversion: Evaluation using ambient
cloud droplet size distributions, W. C. Hsieh et al., JGR, 2009
“In this study, we evaluate eight autoconversion parameterizations against integration
of the Kinetic Collection Equation (KCE) for cloud size distributions measured during the
NASA CRYSTAL-FACE and CSTRIPE campaigns. KCE calculations are done using
both the observed data and fits of these data to a gamma distribution function; it is found
that the fitted distributions provide a good approximation for calculations of total
coalescence but not for autoconversion because of fitting errors near the drop-drizzle
separation size.”
Measured DSD
with gamma
distribution fits
Generating supersaturations to create clouds
• So far, we have focused on generation of supersaturation in an air parcel (really, COOLING
that results in supersaturation generation) by adiabatic expansion. In general,
Updraft speed
• For vertical lifting,
• And using mole fraction of total water
that is liquid (yL):
Heating due to
condensation
• But other cooling mechanisms exist, in addition to uplift:
• Radiation
• Conduction
• Mixing
Cooling due to
expansion
Isobaric, diabatic cooling
• Typical case: Earth’s surface radiates energy to space under clear skies at night
• Air in contact with surface loses thermal energy by conduction, and cools neighboring air parcels by
mixing (dT/dt)
• If moist air cools below its dew point, a radiation fog is created
• Advection fog: moist warmer air flows over cooler surface (e.g., cold lake)
Isobaric, adiabatic mixing
• Typical case: contrails (warm, moist engine exhaust + cold ambient air)
Notice both starting
points were
undersaturated
-- but mixing can
produce
supersaturations over
wide range of mixing
fraction
Cloud properties
http://www-das.uwyo.edu/~geerts/cwx/notes/chap08/moist_cloud.html
Table 2. Observed typical values for the properties of clouds. The values are merely modal-means. The range of
observed values is quite large.
The radius of cloud droplets is r (microns), the effective optical radius optically is r', N is the number of
droplets per cubic centimetre, L is the liquid water content of the cloud (g/m3).
For all clouds, the level of observation is just below the freezing level, except for fog and cirrus. Cirrus consists
entirely of ice crystals, and the values shown in this table are liquid equivalents (Source: (3,4)).
Some Useful (Ballpark) Values (Table 15.3, Seinfeld & Pandis)
Cloud Type
Updraft velocity
(m s-1)
Maximum
supersaturation (%)
Continental cumulus
~1 – 17
0.25 – 0.7
Maritime cumulus
~1 – 2.5
0.3 – 0.8
~0 – 1
~0.05
--
~0.1
Stratiform
Fog
Marine boundary layer
Subsidence
creates warming
that caps the BL
Radiative cooling
(creates negative
buoyancy at cloud top)
and entrainment (grows
against subsidence)
force the circulations
Middle: notice that strong drying means VPT in downdraft can
be warmer than updraft – cloud has to try to compensate
Left case: Air is
cooled, and
condensate lost to
entrainment of dry
air – downdraft
cloud base slightly
higher than updraft
Right: effect of
drizzle is similar to
that of strong
entrainment; can
stabilize BL which
slow circulation