Cumulus Dynamics

Stull’s cu classification

“Passive” important To radiation via cld cover

“Active” transport heat And moisture

“Forced” greatThermal markers!

Marine tradewind cu sounding

Mixed layer

Transition Layer

An ensemble view of tradewind cu

Velocity standard deviations

Vertical momentum fluxes

U-variances

W-variances

Specific humidity variances

Model underestimates moisture variancesSuggests a mesoscale contribution

____-u’w’

___U’q’

Virtual theta-e flux

TKE

Figure 7.12. (a) Frequency-weighted composite q-spectrum. The data were obtained from nine runs by the UK C130 at an altitude of 150 m.$ (b) As for (a), but for the w-spectrum. (c) As for (a), but for the wq- cospectrum. [From Nicholls et al. (1982)].

Peak at 10km

Specific Humidity W-Spectrum

Moisture Flux

Peak at 700m

Figure 7.13. Cartoon of trade-wind boundary layer from large-eddy simulation. Heights of cloud base, level of maximum t gradient (inversion height), and maximum cloud penetration depth are indicated, as are subcloud layer and inversion-level values of thermodynamic quantities. Cloud water contents are averaged over cloudy points only, with adiabatic liquid water contents indicated by the dash-dot line. The far right panel shows cloud fraction, which maximizes near cloud base at just over 5%. [From Stevens, 2005.].

Betts mixed layer model of cu

Entrainmentrate Detrainment

rate

• This explains how HOC’s which do not represent entrainment can still represent fluxes in cu layer well

• Flux divergences which they represent essentially accounts for detrainment

Summary

• Cu moisten the cloud layer and dry the subcloud layer

• That is moistening by detrainment dominates over subsidence drying

• Lower part of cloud layer is warmed and upper part is cooled

• Evaporative cooling and radiative cooling near cld top maintain the trade inversion against subsidence warming

• Moistening and destabilization by small cu favors the development for deeper towering cu

Cartoon of tradewind BL

Towering cu in the tradewind environment

Fig. 7.15

Inversion near0C

• Cu that penetrate stable layer often glaciate and experience a boost in heating from freezing and ice vapor deposition

• Some cu generate shelf-clouds as mass divergence caused by reduced buoyancy drives detrainment

Possible causes of stable layer

• Strongest near MCSs suggesting remnants of melting by snow and ice

• Stable layers may be remnants of gravity waves or buoyancy bores emanating from MCSs; could be focused near 0C by stable layer produced by melting in MCSs and thereby communicate the stabilizing effects of melting over a large area

Cloud fraction

• LES, HOC, mass flux models predict cloud cover by BL eddies which scale with Zi

• However, we have seen that moisture variances scale with mesoscale eddies of the order of 10km. Thus cloud cover by BL models is likely underpredicted

• Examples of mesoscale eddies are Pockets of open cells(POCs) or rifts

Cloud Organization

Approach generally based on analog between laboratory fluid convection and cloud organization observed from satellite or aircraft.

Cellular convection closed cells.

Open cell(doughnuts)

Cloud organization

Open cells

Closed cells

Fig. 7.17

Open cells

Cloud streetsgreat for soaring!

Cloud lines

LongitudinalRoll clds

Transverse Roll clds

Cloud Streets or Longitudinal Rolls

• Preferred in environment exhibits relatively unidirectional wind profiles, that is strongly curved.

Illustration of curvature in wind profile favoring

longitudinal rolls

• Lengths: 20-500 km• Spacing between bands 2 to 8

km.• Width/height ~2 to 4 maybe 6.• Vertical shear 10-7 to

10-6cm-1s-2.• Orientation: parallel 2 to 15o to

right of at top of boundary layer.

• Deardorff: rolls predominant when

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3*

4.5 25;

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hto

L

U TL

kgw T

Surface Heat flux

Role of Gravity Waves

Clark et al. and Kuettner et al. suggest that waves excited by cu feedback on ABL causing changes in cloud spacing and organization.

- Implication to shallow LES models.

Preferred New Growth on Upshear Flank

Upshear movement of wave is slow relative to cu yielding region of ascent for longer period of time near cloud boundary relative to downshear where ascending branch moves quickly away.

More on Gravity waves and cu

Bretherton and Smolarkiewicz (1989; JAS, 740) performed 2D NWP simulations of cu interactions with environment. They also performed 2D linear wave solutions to explain results.

The sounding they used exhibits a deep layer of conditional instability extending up to and above cloud base.

Throughout the cloud layer the sounding is close to, but not exactly neutrally buoyant with respect to the moist adiabat.

They found an ever-widening region in which environmental flow was steadily toward cloud at some levels and away from cloud at other levels.

This, they showed to be a response to the variation with height of buoyancy averaged across the cloud with respect to undisturbed environment.

The v in cloud was close to that of a parcel lifted reversibly from near cloud base. The v profile in environmental was somewhat different leading to +B(z) at some levels and –B(z) at others.The linear model predicts outflow where B(z) decreases with height.

v

Outward propagating G-waves excited by buoyancy source creates vertical displacements in the environment in a widening region around the cloud which makes B(z) of environment ~ buoyancy in the cloud.

The G-waves excited by buoyancy imbalance between cloud and environment compensates for vertical mass fluxes in the cloud.

The G-wave response to a cu field leads to a buoyancy adjustments time (T1) in which the environment approaches buoyant equilibrium with the clouds. This is much shorter than mixing time T2 for a tracer concentrated at a level to become homogenized through the layer.

Observed characteristics of individual cu

Observed cu

Fig. 7.22c,d

Fig. 7.23

Observed rl/adiabatic

Strongest w upshear

Sailplane obs of cu

Horizontal cross sections

Simulated P-field

Tethered balloon obs of cu

Fig. 7.29

Fig. 7.30

Schematic of cu growing in shear

Summary of features of cumulus clouds

• r/ra decreases rapidly with height.• Values of LWC > ra are sometimes

observed in small samples.• Low values of LWC occur randomly

throughout the cloud.• The edges of the cloud are usually

sharp. _| |_• Detainment from clouds occur,

particularly on the downshear side.• Lapse rate in cloud differ little from

the environment.• Observations and model results

suggest that vertical rather than horizontal mixing strongly affects cloud development and dilution of Cu.

Theories of entrainment

Thermal or bubble model

Jet Model

Thermal model

Let Mc be mass of the cloud:

1

3 0.6

cc

c

dM b

M dz R

b

Steady Jet

1

2 0.2

mj

m

dF b

F dz R

b

Mass flux

Mass of bubble

• Need eqs 7.15 and 7.16

• According to lateral entrainment concept the thermodynamic properties at a given level should be a mixture of cloud-base level properties and air entrained at all levels below that level.

Squires (1958) proposed that cu clouds are diluted from the top down.

Paluch Diagram

Uses conservative variables rT and wet equivalent potential temperature q.

If air at one level of a sounding is mixed with air from another level in various proportions, the rT, q

points should lie along a straight line connecting the q, RT points at the two levels.

Paluch diagram

Since the in-cloud data form a straight line, it suggests mixing occurs between two levels, in this case cloud base and cloud top!

It is argued that most parcels within a cloud are a blend of cloud-base and cloud top air. The q, RT analysis suggests that at a given sampling level the air appears to originate from that level to about 1 km higher. This supports the idea that mixing at cloud top prevails.

Blyth et al. (1988) interpret their A/C measurements in terms of a “thermal-like” model in which environmental air enters the cloud top, descends along the flanks of the thermal core, and then enters into the sides (laterally) on the trailing portions of the thermal. Behind the thermal is a “wake” of cloudy air with weak w’s.

This model contains both “top” and “lateral” entrainment concepts.

Blyth conceptual model

Two schools of entrainment

• dynamic school of entrainment

• CTEI based concept

dynamic school of entrainment

• Kelvin-Helmhotz type instabilities generated by local and thermal-scale shears at the cloud-clear air interface

• Rayleigh-Taylor type of instabilities in which small scale vortical circulations are generated by baroclinic torques generated by vertical and horizontal density gradients

CTEI based concepts

• entrainment is induced by buoyancy differences associated with phase changes as cloudy air mixes with dry environmental air

• This concept has lead to the formulation of what are called buoyancy-sorting models(Raymond, 1979; Raymond and Blyth, 1986; Emanuel, 1991) in which parcels of air gain negative buoyancy and aggregate at their level of neutral buoyancy.

• Grabowski(1995) for example argues that entrainment is caused by these interfacial instabilities while buoyancy reversal is an effect of entrainment.

• He argues that the CTEI-based concept is not the primary driver of entrainment

• Recent LES modeling results of simulations of tradewind cumuli by Jiang and Feingold(2006), Xue and Feingold(2006), Xue et al., 2007), Cheng et al.(2008) suggest that variations in CCN concentration effect entrainment.

• This work supports the idea that entrainment is controlled in part by the CTEI concept. That is not to say that entrainment is not initiated by dynamic instabilities associated with shears along the cloud boundaries but that, at the very least, evaporation of drops mixing with the entrained air amplifies the entrainment process.

• the importance of vertical shear of environmental winds as a mechanism of enhancing dynamic forcing of entrainment, relative to a no-sheared environment, versus CTEI type forcing of entrainment has yet to be quantified.

• As environmental wind shear is increased will dynamically-driven entrainment be enhanced to such an extent that aerosol effects on entrainment will be masked or relegated to secondary importance?

• we need to quantify the relative roles of large eddies versus small eddies to the entrainment process. The evidence is compelling that small eddies, less than 10m scales, initiate the entrainment process, but is it necessary to explicitly resolve eddies on such small scales in order to represent the bulk thermodynamic and dynamical properties of cumuli properly?

Example of collapsing bubble causing

detrainment

Role of Precipitation

Unloads water from top reduces water loading.

Cools sub-cloud layer—causing divergence and lifting of moist, sub-cloud air.

Precipitation and Entrainment

Precipitation will settle down-shear, causing further descent in that region, enhance low pressure, and accelerate entrainment.

Role of Ice Phase

Fig. 7.36

Fig. 7.37

Cloud merger-no shear

Cloud merger-shear

No shear schematic from simulation

Shear schematic from simulation

Mesoscale convergence

• Cloud merger favored when low-level convergence is present

• Low level convergence favors larger storms and heavier rainfall

• Observations suggest low-level convergence preceeds development of radar echos by as much as 90min

• The major factor determining the amount of rainfall is the size of the area of convergence