UNRESOLVED ISSUES
1.
Spectral broadening through different growth histories
2.Entrainment and mixing
3.
In-cloud activation
Spectral broadening
/39 2 Figures: Brenguier and Chaumat, JAS 2001
Observations show broad droplet spectra while the idealized model of droplet growth in an adiabatic convective cell predicts narrow spectra.
The 𝑟! Φ! distribution (solid line) for measurements during SCMS (Small Cumulus Microphysics Study, Florida 1995).
Comparison with the adiabatic reference (dot–dashed line).
The initial reference spectrum is represented by a dot–dashed line on the left.
/39 3
𝑑𝑟
𝑑𝑡 = 𝜉𝑆 − 1
𝑟 , 𝜉 = 1
𝐹! + 𝐹"
𝑛 𝑟, 𝑡 = 𝑟
𝑟# − 2𝜁𝑡𝑛$ 𝑟# − 2𝜁𝑡 𝑡 = 𝑧
𝑢
𝑛$ 𝑟$ cloud base
/39 4
𝑑𝑟
𝑑𝑡 = 𝜉𝑆 − 1
𝑟 , 𝜉 = 1
𝐹! + 𝐹"
𝑛 𝑟, 𝑡 = 𝑟
𝑟# − 2𝜁𝑡𝑛$ 𝑟# − 2𝜁𝑡 𝑡 = 𝑧
𝑢
𝑛$ 𝑟$ cloud base
1,2 0,8 u (m/s)
/39 5
𝑑𝑟
𝑑𝑡 = 𝜉𝑆 − 1
𝑟 , 𝜉 = 1
𝐹! + 𝐹"
𝑛 𝑟, 𝑡 = 𝑟
𝑟# − 2𝜁𝑡𝑛$ 𝑟# − 2𝜁𝑡 𝑡 = 𝑧
𝑢
𝑛$ 𝑟$ cloud base
1,2 0,8 u (m/s)
/39 6
𝑑𝑟
𝑑𝑡 = 𝜉𝑆 − 1
𝑟 , 𝜉 = 1
𝐹! + 𝐹"
𝑛 𝑟, 𝑡 = 𝑟
𝑟# − 2𝜁𝑡𝑛$ 𝑟# − 2𝜁𝑡 𝑡 = 𝑧
𝑢
𝑛$ 𝑟$ cloud base
1,2 0,8 u (m/s)
/39 7
𝑑𝑟
𝑑𝑡 = 𝜉𝑆 − 1
𝑟 , 𝜉 = 1
𝐹! + 𝐹"
𝑛 𝑟, 𝑡 = 𝑟
𝑟# − 2𝜁𝑡𝑛$ 𝑟# − 2𝜁𝑡 𝑡 = 𝑧
𝑢
𝑛$ 𝑟$ cloud base
1,2 0,8 u (m/s)
/39
𝑛$ 𝑟$ 8
cloud base
1,2 0,8 u (m/s)
Spectral broadening through different growth histories
/39 9 Figure courtesy of S. Lasher-Trapp
• Simulation of a small cumulus, illustrating the idea of cloud-droplet growth through large- eddy hopping.
• The figure shows the cloud water field and a small subset of droplet trajectories arriving at a single point at the upper part of a cloud.
• The trajectories are colored according to the liquid water content encountered.
• The variability of the vertical velocity across the cloud base already results in some
differences in the concentration of activated cloud droplets at the starting point of the trajectories.
• There are also relatively small-scale changes in color along the trajectories, highlighting variable environments in which the droplets grow.
Large eddy-hopping
/39 10 Figure by Katarzyna Nurowska
ENTRAINMENT AND MIXING OF ENVIRONMENTAL AND
CLOUDY AIR
RICO (Rain in Cumulus over the Ocean)
/39 12 Medeiros and Stevens 2011
The right panel shows estimates of cloud fraction from the lidar (lines) using different detection thresholds (as indicated in red, with the black line being the 22 dBZ threshold). The filled circles show cloud fraction from in situ measurements near cloud base (where the sampling was most random) and along the leg at 4.5 km. Cloud water measured in the sub-cloud layer is from precipitation.
Cloud water (left) and fraction
(right) profiles from the C130 flights during RICO. The sampling included all fligts legs below 2 km for which good data was available. Shown onthe left is the interquartile
wariability (25 and 75%, whisker), mean (gray circle) and median (black circle) of cloud-water.
/39 13
cloud core samples (ql>0, θv’>0 ) cloud samples (ql>0)
cloud parcels become negatively buoyant when cooling due to evaporation of cloud droplets due to entrainment drying exceeds entrainment warming
/39 14
Entrainment
/39 15
Homogeneous mixing N=const
r $
Inhomogeneous mixing N $r =const
q=qs
q=qs
q=qs q<qs
q<qs q=qs
q=qs q=qs
/39 16
Homogeneous mixingInhomogeneous mixing
/39 17
n - number of droplets
extremly inhomogeneous mixing
homogeneous mixing inhomogeneous mixing
𝑚 = 4
3𝜋𝜌%𝑛𝑟&'
𝑟&' = 3 4𝜋
𝑚 𝜌% 6 1
𝑛
if m=const 𝑟&'~)(
Homogeneous mixing
/39 18
Vc , qc Ve , qe Nc=n/Vc Ne=0
concentration
mixing coefficient concentration after the mixing event water vapor sepcific humidity after the mixing event amount of water to be evaporated until the saturation is reached
𝜒 = 𝑉* 𝑉* + 𝑉+ 𝑁 = 𝜒 6 𝑁*
𝑞 = 𝑞*𝜒 + 1 − 𝜒 𝑞+ 𝛿𝐿𝑊𝐶 = 𝑞, − 𝑞 𝜌
𝐿𝑊𝐶 − 𝛿LWC = 4
3𝜋𝜌%𝑁𝑟&' ⟶ 𝑟&' = 𝐿𝑊𝐶 − 𝛿𝐿𝑊𝐶
43 𝜋𝜌%
6 1 𝑁
𝑁 = 𝑛
𝑉* + 𝑉+
/39 19
/39 20
/39 21
/39 22
/39 23
/39 24
𝐿𝑊𝐶 = 4
3𝜋𝜌%𝑁𝑟&' 𝐿𝑊𝐶-! = 4
3𝜋𝜌%𝑁-!𝑟&,-!'
𝐿𝑊𝐶
𝐿𝑊𝐶-! = 𝑁
𝑁-! 6 𝑟&' 𝑟&,-!'
𝑟&'
𝑟&,-!' = 𝐿𝑊𝐶 𝐿𝑊𝐶⁄ -!
𝑁 𝑁⁄ -!
Which type of mixing happens in clouds?
/39 25
Turbulence defines how quickly a mixture of dry environmental air and cloudy air is homogeneised " mixing time scale (tmix)
Evaporation " evaporation time scale (tevap).
tmix << tevap homogeneous mixing
tmix >> tevap extremly inhomogeneous mixing
/39 26 Dorota Jarecka; PhD thesis
evap mix
30 v vf3
0 f
30 v vf3
0 f
r d r
N d N
1 r
d r N d N
t t c
=
÷÷ ø ö çç
è æ
÷÷ø çç ö
è æ
@
÷÷ ø ö çç
è æ
÷÷ø çç ö
è æ
=
Slope coefficient
/39 27
Inhomogeneous mixing
a
÷÷ø çç ö
è
= æ
co 0 cf
f q
N q N
a= 0 : Nf=N0 homogeneous mixing
a =1: extremly inhomogeneous mixing
/39 28 a
a a a
-
÷÷ø çç ö
è
= æ
÷ ®
÷ ø ö çç
è
= æ
÷÷ø çç ö
è
= æ
1 3
0 v 0 vf 3 f
0 v 0
vf3 0 f
f
co cf 0 f
r N r r N
N r N N
N
q N q N
In the model, during one time step the value of the mean volume radius doesn’t change a lot; one can express is as a Taylor series for (rf/r0)3=1.
a c a
a a
= -
÷÷ ø ö çç
è æ
÷÷ø çç ö
è æ
=
úú û ù êê
ë é
÷÷ ø ö çç
è
æ ÷÷ø - çç ö
è æ + -
=
1 r
d r N d N
r 1 r 1 1
N N
30 v vf3
0 f
3 0 v 0 vf
f
evap mix
evap mix
1 t t t t
a = +
/39 29 Dorota Jarecka, PD thesis
Shallow convection
BOMEX (Barbados Oceanographic and Meteorological Experiment)
homogeneous
mixing inhomogeneous
mixing
/39 30 Dorota Jarecka, PD thesis
Stratocumulus
(EUCAARI IMPACT)
/39 31
Dorota Jarecka, PhD thesis
/39 32 Dorota Jarecka, PhD thesis
Stratocumulus (EUCAARI IMPACT)
inhomogeneous mixing
homogeneous mixing
/39 33 Dorota Jarecka, PhD thesis
homoheneous
mixing inhomogeneous
mixing
IN-CLOUD ACTIVATION
RICO
(Rain in Cumulus over the Ocean)
/39 35
Arabas et al. GRL 2009 Gerber et al., JMSJ, 2008
How is it possible that the dilution of the
cloud water content is NOT accompanied by the dilution of the droplet concentration?
/39 36
How is it possible that the dilution of the
cloud water content is NOT accompanied by the dilution of the droplet concentration?
/39 37
In-cloud activation
(i.e., activation above the cloud base)!
/39 38 Slawinska et al., JAS 2011
LES modeling with 2-moment microphysics
/39 Grabowski, W.W. and S. A. McFarlane, 2007: Optical properties of shallow tropical cumuli derived from 39
ARM ground-based remote sensing, Geophys. Res. Let.
