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.
• **This 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 Sband 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 – momentweight fall speeds are calculated based on prognostic
moments (0th, 3rd, 6th) & every drop falls @ same speed.
Pure Sedimentation
Sedimentation of q:
Sedimentation of Ntot:
Sedimentation of Z:
Pure Sedimentation
Excessive size sorting
No drops reaching
the ground
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 (3km 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
ZH
ZDR
Excessive size sorting
No drops reaching
the ground
KDP
RhoH
V
Wind Shear – Single Moment Bulk
ZH
ZDR
KDP
RhoH
V
Wind Shear – Two-Moment Bulk
ZH
ZDR
Excessive size sorting
Excessive size sorting
No drops reaching
the ground
KDP
RhoH
V
Wind Shear – Two-Moment Bulk
Overestimate in
Kdp due to an
overprediction
of smaller &
medium sized
drops
ZH
ZDR
KDP
RhoH
V
Wind Shear
Difference
Fields
•
•
•
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.
ZH
ZDR
RhoH
V
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.