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 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 (0th, 3rd, 6th) & every drop falls @ same speed.

Pure SedimentationSedimentation 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 (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

No drops reaching the ground

Excessive size sortingZH ZDR

KDP RhoHV

Wind Shear – Single Moment Bulk

ZH ZDR

KDP RhoHV

Wind Shear – Two-Moment Bulk

No drops reaching the ground

Excessive size sorting

ZH ZDR

KDP RhoHV

Excessive size sorting

Wind Shear – Two-Moment Bulk

ZH ZDR

KDP RhoHV

Overestimate in Kdp due to an overprediction

of smaller & medium sized

drops

Wind Shear Difference

FieldsZH ZDR

RhoHV

• 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.