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Entrainment rate from buoyancy com
velocity as B=W/c where c=120 s
Center for
Entrainment rates for deep convective cores found by exploiting the linear relationship
of
Multiscale Modeling
of
Atmospheric
Process
vertical velocity to buoyancy
Ian B. Glenn and Steven K. Krueger
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University
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Lake
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[email protected]
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1371 Campus Del. ! Colorado State University ! Fort Collins, Colorado
Best fit entrainment rate given B and W
Introduction
1
A National Science Foundation Science a
Entrainment
ratebe
fromapplied
buoyancy to
computed
from vertical
Can
method
observations?
CMMAP conducts research and promotes the education of a diverse
scientific workforce. CMMAP communicates its findings to the general
public, to policy makers, and to centers that predict weather and
climate.
velocity as B=W/c where c=120 s
• Consider the buoyancy and vertical velocity profiles for each active 3D
cloudy updraft
• What fractional entrainment rate for a parcel gives the best fit to the 3D
cloudy updraft profile of vertical velocity?
The Giga-LES
• System for
10^2
10^0
10^6
10^8
10^10
Volume (m3)
10^12
Figure 2. Log-log frequency distribution of 3D cloudy updraft volumes. We
ignore the group of volumes to the left of the dashed black line as they are
composed of only a few model grid points. The cut-off volume is that of a
cube 450 m on each side.
Partition cloudy updrafts into two groups
Dissipating
Active
•Life-cycle stage of the
convection?
•Low cloud bases: growing and
mature convective updrafts
•Elevated cloud bases: dissipating
stage of updraft
•Define “active” as 3D cloudy
updrafts with cloud base < 1 km
Figure 3. Log frequency of 3D cloudy updrafts vertical extent vs. cloud base
height. The clouds outlined in the lower black rectangle are representative of
active cumulus convection, with bases below 1 km.
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4
0.4
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www.cmmap.org
0
0
Height ( km )
Height ( km )
3 Mean
Error:
2.5
0.5 m/s
Lamda:
2
−1
0.38 km
1.5
1
0.5
Mean
4 Error:
0.8 m/s
3 Lamda: −1
0.41 km
2
1
3 km
5 km
0
−2
0
2
4
6
Vertical Velocity ( m/s ) and Buoyancy( 10−2 m/s2 )
0
−4
−2
0
2
4
6
Vertical Velocity ( m/s ) and Buoyancy( 10−2 m/s2 )
(a)
(b)
12
8
Mean
Error:
6 0.7 m/s
Lamda:
−1
0.41 km
4
Mean
10 Error:
2.9 m/s
8 Lamda:
0.12 km−1
6
4
2
8 km
0
−2
0
2
4
6
Vertical Velocity ( m/s ) and Buoyancy( 10−2 m/s2 )
2
12 km
0
−10
−5
0
5
10
Vertical Velocity ( m/s ) and Buoyancy( 10−2 m/s2 )
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2.0
Fractional
entrainment
rateEducation
(km−1)
Melissa Burt
, CMMAP
& Diversity Manager
1.8
1.6
Teacher Resource
1.4
1.2
8
1
Helping teachers
and students
reach0.8for the sky!
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2
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0
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Fractional entrainment rate (km−1)
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(a)instead of the known buoyancy profile we use B=W/(120
(b)(c)s) +
Figure
6.
Same
as
Fig.
5,
but
1371 Campus Del. ! Colorado State University ! Fort Collins, Colorado
Drag. The known drag profile is used to illustrate a best possible case of using this method.
• An estimate of the drag force is
essential for this method
• Four example cloudy
updrafts are shown,
note different cloud top
heights
• Cloud average W profile
in red
• Many possible W
profiles are calculated
for a range of λ, best fit
plotted in blue
• “Unloaded” thermal
buoyancy black dashed
• “Loaded” density
buoyancy B solid black
Summary
A National
Science
Foundation
Sciencethe
and Technolog
Figure 1: The entrainment
rate
that
produces
best fi
given
approximate buoyancy profile as input. In
• It aisB=W/c
encouraging that precip. mixing
drag force is added to the buoyancy profile. In (b) and (d
ratio varies nicely with CTH
note the horizontal scale is increased from 2 to 5 km−1 . In (
the average mass of precipitating condensate per kg of clo
the last 13 hourly snapshots of GigaLES are used.
• 3D cloudy updrafts are defined in a large domain LES of deep
convection. We (c)
select those with cloud base < 1 (d)
km as “active clouds”
1
Figure
1: The
entrainment
rate that
produces parcel
the bestmodel
fit to the
profile cloud
when
show
that a simple
entraining
forcloud
eachWactive
• We
given a B=W/c approximate buoyancy profile as input. In (a) and (c), the actual known
can
partially
explain
the
distribution
of
cloud
top
heights
drag force is added to the buoyancy profile. In (b) and (d), no drag force is added, and
−1 . In (c) and (d), the colors represent
note•the
horizontal
scale
is
increased
from
2
to
5
km
After Alison Stirling of the Met office and others, we note average
the average mass of precipitating condensate per kg of cloud air. All active clouds from
vertical velocity profile is proportional to average unloaded buoyancy
the last 13 hourly snapshots of GigaLES are used.
profile in the active clouds
• Using this estimate for unloaded buoyancy, dual doppler radar
retrievals of vertical velocity could theoretically then be used to solve
(c)
(d)
Entrainment
rateblack),
from
buoyancy, vertical
velocity,
Figure 4. Profiles of 3D cloudy updraft average loaded buoyancy 1
(black),
unloaded buoyancy (dashed
and vertical
for λ, given
an estimate of drag
Figure
3: Profiles
of average
buoyancy
Bu (dashed
velocity
(red). Best
fit parcelunloaded
model vertical
velocity
is plottedblack),
in blue.average loaded buoy1
for active clouds in the GigaLES
ancy Bd (black), and average vertical velocity W (red), where the average is taken over
Using the known drag as a “best case” gives encouraging results
•
each level of the cloud. The vertical velocity calculated using a parcel model that uses
Entrainment rate λ from best-fit parcel model of cloudy updraft W
B as input is plotted in blue. The parcel model is evaluated multiple times for different
d
assumed constant fractional entrainment rates, and the case with the minimum
sum of
14
squared errors (SSE) between parcel W and cloud W is the one shown. The associated
12
entrainment rate (lamda) and the square root of SSE normalized by the number
of levels is
noted on each figure. The four clouds were selected from the group of clouds having cloud
10
top loaded buoyancy close to zero, cloud base below 2 km, and cloud top height within 1
km of 3, 5, 8, and 12 km respectively.
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1
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References
Arakawa, A., 2004: The cumulus parameterization problem: Past, present, and future. J. Clim., 17,
0.4
2493-2525.
4
Heus, Thijs, Gertjan van Dijk, Harm J. J. Jonker, Harry E. A. Van den Akker, 2008: Mixing in shallow cumulus
0.2
2
5
clouds studied by lagrangian particle tracking. J. Atmos. Sci., 65, 2581–2597.
Khairoutdinov, M., S. K. Krueger, C.-H. Moeng, P. A. Bogenschutz, and D. A. Randall,
0
0
0.4
0.8
1.2
1.6
2.0
2009: Large-eddy simulation of maritime deep tropical convection. J. Adv. Model. Earth Syst., 1.
−1
Fractional entrainment rate (km )
LeMone, Margaret A., Edward J. Zipser, 1980: Cumulonimbus Vertical Velocity Events in GATE. Part I:
(a)
(b)Diameter, Intensity and Mass Flux. J. Atmos. Sci., 37, 2444–2457.
Figure 5. On the left, frequency vs cloud top height of parcel model entrainment rate that produces the best fit to the
Lin, C., and A. Arakawa, 1997: The macroscopic entrainment processes of simulated cumulus ensemble.
cloud W profile. On the right, the average precipitating condensate
for
the
clouds
in
each
λ
and
cloud
top
height
bin.
Figure 1: The entrainment rate that produces the best fit to the cloud W profile when
Part I: Entrainment sources. J. Atmos. Sci., 54, 1027-1043.
• Maximum cloud top height at a
particular λ decreases with increasing λ
• What explains the range of cloud top
heights for the same λ? Life-cycle
stage? Are those clouds still growing?
6
C
[email protected] ! (970) 491-8706
Cloud Mass Weighted Avg. Precip (g/kg)
10^4
3D Volumes
Cut−off size
…gives the
best fit to the
known W
profile (min.
RMS error)
Cloudy Updraft Vertical Velocity
Parcel Model Vertical Velocity
Cloud Top Height (km)
Frequency
10^6
• Contiguous volumes
• We use a cloudy updraft core
definition similar to that used in
Lemone and Zipser (1980)
• Vertical velocity (w) > 1 m/s and
cloud water/ice mixing ratio (qn) > 0.1
g/kg
• Largest volume is equivalent to a
cube 10 km on each side
Iterate to find
the fractional
entrainment rate
that…
Using level average
density buoyancy
from cloudy updraft
core
Height ( km )
Identify 3D cloudy updrafts
1
2
Height ( km )
Figure 1. SHDOM visualization of light scattering in liquid and ice water
mixing ratio fields from the Giga-LES. The horizontal domain visualized above
is 20 km x 20 km, about 1/100th of the total domain area.
Atmospheric Modeling
(SAM)
• Horizontal domain of
204.8 km x 204.8 km
• ∆x = ∆y = 100m
• ∆z = 50m to 100m
• 10^9 grid cells
• A “virtual field
campaign”
(Khairoutdinov et al.
2009)
• Validated against
observations (Lemone
and Zipser 1980)
8
Cloud Top Height (km)
• What determines the distribution of cloud top heights (Arakawa 2004)?
• The Giga-LES is especially well suited to studying entrainment in deep
convection because of its large domain and turbulence resolving 100 m
horizontal resolution.
(a)
Cloud Mass Weighted Avg. Precip (g/kg)
Solve for B assuming W = (B - Drag) * 120 s
Log10 Number of Clouds
Parcel Model for Vertical Velocity
Cloud Top Height (km)
Motivations
Clouds are one of the most important parts of the climate system and
control cycles of energy, water, motion, and chemistry. The climate
models that scientists currently have the technology to create do not
14
completely
represent cloud processes; the models are
too coarse to 14
1.8
accurately portray clouds and cloud movement, so it is difficult to
understand
and predict changes in global climate. Scientists
have 12
1.6
12
recently discovered a way to address these issues. CMMAP is
1.4to more accurate
developing
a revolutionary new approach that will lead
10
10
simulations and a better understanding of global climate
1.2 change.
given the cloud buoyancy profile as input. In (a), the density buoyancy is used (weight
of•all cloud and precip. condensate included). In (b), the thermal buoyancy is used (only
Average precipitating condensate is a
ACKNOWLEDGEMENT.
virtual temperature effects from vapor included). The colors
represent the average massThis
of material is based upon work supported by the National
strong
function
of
cloud
top
height,
but
Science
and Technology Center for Multi-Scale Modeling of
only precipitating condensate per kg of cloud air. All active
clouds Foundation
from the lastScience
13 hourly
not ofofλGigaLES are used.
Atmospheric Processes, managed by Colorado State University under cooperative
snapshots
agreement No. ATM-0425247.