Size Sorting in Bulk & Bin Models
•
Onset of
precip
–
development of particles large
enough to sediment relative to cloud droplets &
ice crystals.
•
Larger particles tend to fall faster.
•
Differential Sedimentation (D.S.)
•
Atmospheric flows (e.g. updrafts) can prolong
D.S. due to the removal of small drops upward &
exhausted through the anvil region.
Size Sorting
•
In rainfall,
Zdr
tends to increase w/ increasing
Zh
because heavier rain tends to have large conc. of
bigger drops.
•
Leads to an increase in both
Zdr
and
Zh
.
•
Thus, high
Zdr
values alone are not sufficient to
identify size sorting.
•
**
T
his true for interpretation of nearly all
polarimetric
signatures**
•
Review of common size

sorting on
polarimetric
variables w/ the use of simplistic bin models.
Size Sorting in Bulk and Bin Models
•
Fall speed increases w/ increasing drop diameter
•
From
Brandes
et al. (2002):
•
Matches historical observations and recent
observations from
Thurai
&
Bringi
(2005).
•
Power law from Atlas &
Ulbrich
(1977)
substantially overestimates fall speed of large
drops (>6mm), while bulk microphysical
schemes slightly underestimate
Vt
for D>6mm.
Bin
vs
Bulk Microphysics
•
Bulk Schemes
–
Particle size distributions are
assumed to have a shape describe by an analytic
function (e.g. three parameter gamma distr.)
•
Previous studies (Table 1) have demonstrated
that microphysics schemes with only one
prognostic moment are unable to capture D.S.
•
Bulk models can better match Bin models for
D.S. after an extended amount of time.
Bin
vs
Bulk Microphysics
•
Spectral or Bin Microphysics
–
Each particle size is
assigned to a “bin” and each bin is assigned its own fall
speed.
•
Thus Bin models are able to explicitly capture D.S. much
better than bulk schemes, particularly during the initial /
early time periods.
•
None of the studies in Table 1 has investigated the
maintained size sorting possible by updrafts or vertical
wind shear.
•
Investigations of
supercell
storms have revealed repetitive
polarimetric
radar signatures (
Zdr
Arc,
Zdr
Column) that
are seemingly characteristic of such storms (wind shear,
air flows, buoyancy, life cycle)
Bin
vs
Bulk Microphysics
•
Spectral or Bin Microphysics
–
Each particle size is
assigned to a “bin” and each bin is assigned its own fall
speed.
•
Thus Bin models are able to explicitly capture D.S. much
better than bulk schemes, particularly during the initial /
early time periods.
•
None of the studies in Table 1 has investigated the
maintained size sorting possible by updrafts or vertical
wind shear.
•
Investigations of
supercell
storms have revealed repetitive
polarimetric
radar signatures (
Zdr
Arc,
Zdr
Column) that
are seemingly characteristic of such storms (wind shear,
air flows, buoyancy, life cycle)
Size Sorting Models
•
Models for a particular size soring mechanism
were developed, applied to both bin and bulk
models, & resulting DSDs were converted to S

band
polarimetric
radar variables.
•
Raindrops assumed to be pure water at a T=20
°
C, w/ mean canting angle of 0
°
.
•
Models applied to Pure Sedimentation and
Vertical Wind Shear.
Pure Sedimentation
•
A distribution of raindrops is prescribed at the top of the
domain & drop begin falling at Ti.
•
Fresh drops are continuously replenished at the top of
the domain (“cloud base”) at each time step & domain is
3km tall.
•
Simulate sedimentation of drops in bulk
–
moment

weight fall speeds are calculated based on prognostic
moments (0
th
, 3
rd
, 6
th
) & every drop falls @ same speed.
Pure Sedimentation
Sedimentation of q:
Sedimentation of
Ntot
:
Sedimentation of Z:
Pure Sedimentation
No drops reaching
the ground
Excessive size sorting
Overestimate in
Kdp
due to an
overprediction
of smaller &
medium sized
drops
Vertical Wind Shear
•
Provides nonzero storm

relative flow, allowing
raindrops to be
advected
away from directly
beneath the cloud.
•
Smaller drops encounter storm

relative flow for
longer periods of time & are thus transported
farther downstream.
•
Size Sorting
–
Explains enhancement of
Zdr
along the leading edge of MCSs (
Ulbrich
&
Atlats
2007, Morris et al. 2009,
Kumjian
&
Ryzhkov
2009,
Teshiba
et al. 2009)
Vertical Wind Shear
•
2

D
model
similar
to
previous
1

D
except
a
vertical
wind
profile
is
introduced
.
•
Storm

relative
winds
increase
linearly
toward
the
ground
from
0
m/s
@
cloud
base
(
3
km
AGL)
to
20
m/s
at
the
surface
.
•
1
km
wide
precipitating
“cloud”
is
placed
at
the
top
left
of
the
model
domain
w/
a
Gaussian
Dist
.
For
the
precip
intensity
pattern
.
•
Raindrop
motion
is
determined
purely
by
advection
and
sedimentation,
governed
by
Eqn
(
10
)
.
Wind Shear
–
Bin Model Results
No drops reaching
the ground
Excessive size sorting
Z
H
Z
DR
K
DP
Rho
H
V
Wind Shear
–
Single Moment Bulk
Z
H
Z
DR
K
DP
Rho
H
V
Wind Shear
–
Two

Moment Bulk
No drops reaching
the ground
Excessive size sorting
Z
H
Z
DR
K
DP
Rho
H
V
Excessive size sorting
Wind Shear
–
Two

Moment Bulk
Z
H
Z
DR
K
DP
Rho
H
V
Overestimate in
Kdp
due to an
overprediction
of smaller &
medium sized
drops
Wind Shear
Difference
Fields
Z
H
Z
DR
Rho
H
V
•
1M
–
Zdr
underestimated nearly
everywhere, especially
near the ground
where size sorting
most pronounced.
•
2M

Overpredictions
in
Zdr
nearly
everywhere.
•
3M
–
Minimal
differences and
generally only slight
underestimates.
Polarimetric
Observations
•
Large
values
of
Zdr
along
Zh
gradient
in
the
leading
edge
of
MCSs
.
•
Zdr
enhancements
found
at
the
base
of
developing
convective
cores
.
•
Zdr
Arc
signatures
in
supecell
storms
due
to
size
sorting
by
vertical
wind
shear
.
–
Zdr
values
in
excess
of
4
dB
which
are
present
outside
the
30
dbZ
Zh
contour
.
–
Strong
wind
shear
in
supercell
environments
•
Light
to
moderately
precipitating
storms
in
an
environment
with
vertical
wind
shear
=
highest
Zdr
at
the
leading
edge
of
a
rain
shaft
along
a
gradient
in
Zh
.
•
Biological
scatterers
differentiate
between
precip
and
biological
scatterers
.
Polarimetric
Observations
Summary
•
Size
sorting
in
bin
models
have
significant
impact
on
polarimetric
radar
variables
•
Differential
sedimentation
can
be
maintained
by
updrafts
and
vertical
wind
shear
.
•
Single
moment
bulk
parameterizations
are
incapable
of
simulating
size
sorting,
and
thus
the
impact
of
D
.
S
.
on
dual

pol
variables
.
–
Significant
overestimates
in
Zdr
,
Zh
,
&
Kdp
•
Double
moment
gets
somewhat
closer
to
bin,
but
often
results
in
over

sorting
or
excessive

sorting
.
•
Three
moment
fairly
close
to
replicating
the
bin
models
for
D
.
S
.
and
the
impact
on
dual

pol
variables
.
•
Size
sorting
can
thus
have
a
tremendous
impact
on
the
assimilation
of
dual

pol
data
into
numerical
models
.
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