A Polarimetric Method for Ice Water Content Determination

1
A Polarimetric Method for Ice Water Content
Determination
Ryzhkov, Zrnic, and Gordon (JAM 98)
2
Motivation

• Existing IWC-Z relationships stink

3
Motivation cont.

• These IWC-Z relationships dont work because they
  cant incorporate the fact reflectivity factor is
  proportional to the product of the IWC and the
  mass of the average ice hydrometeor
• Thus, two independent measures are desirable.
  This can be accomplished with polarimetric
  variables. Ryzhkov, Zrnic, and Gordon (JAM 98)
  used ZDR and KDR

4
Assumptions

• Dry snow, density is a simple function of
  diameter (Matrosov et al.96)
• Rayleigh scattering, derivation from van de Hulst
  81

Lb (1-La)/2
oblate
prolate
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Assumptions cont.

• Low elevation scanning angle
• Matrosov et. al (96) classification of ice
  crystal types

h smaller dimension, L larger dimension
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Derivations

• Relationships between mass and parameters s and
  Re(fh-fv) are derived for each of the 11 crystal
  types using the assumed density verses diameter
  relationship

by observing that
for prolates
for oblates fh fb, fvfa, sh sb, sv sa
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Derivations cont.

• The ratio (sh-sv)/Re(fh-fv) is linearly
  proportional to the mass of the ice particle.
  Interestingly, the value of a3 doesnt vary
  significantly with the type of ice crystal
• The previous 3 equations can be used to derive
  relationships for Zh, KDP, and ZDP

8
Derivations cont.

• IWC is related to drop size distribution, which
  is in turn related to Zh, KDP, and ZDP
• Using the following formula,Zh, KDP, and ZDP can
  be calculated,

and IWC can be derived

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Stability of Derived IWC Equation

• To obtain a generalized IWC equation for all ice
  types, we must ensure that the IWC equation has
  little dependence on ice crystal type. It turns
  out that the value of C1 varies only 20 over all
  the values of d (the dependence of ? on D), and
  the backscattering parameters a1 and b1. A more
  generalized form of the IWC equation is

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Attributes of Derived IWC Equation

• Although one of the original assumptions was low
  elevation angle, the equation still holds for
  higher elevation angles because the ratio KDP/ZDR
  is unaffected (since both parameters have the
  same dependence on elevation angle)
• The equation happens to be insensitive to radar
  calibration errors because the absolute value of
  reflectivity is not involved (rather, a ratio is
  used)
• The equation begins to break down as snowflakes
  aggregate because the shape becomes more
  spherical and ZDR,KDP ? 0 thus small errors in
  ZDR cause large biases in IWC

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IWC Equation Threshold

• There needs to be a threshold minimum value for
  ZDR. At values below this threshold, it can be
  assumed that the IWC estimate is inaccurate.

cold snow, sfc temp lt -5 C
warm snow
Threshold of 0.7 dB
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In Situ Observations

• The best way to find a threshold for ZDR is also
  the best way to find out if the equation works at
  all fly a plane around and take some
  measurements!
• This was done during the VORTEX experiment on May
  21, 1995. A T-28 aircraft flew through an area of
  high KDP in a trailing precipitation area behind
  a squall line, measuring mostly pristine crystals
  and small aggregates at (which conform to the
  best-case scenario for the IWC equation).

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The Results
Z-IWC Relationships
Polarimetric Relationships
Vs.
(using a threshold of 0.7dB for ZDR)
Heymsfield IWC 0.035Z0.51Atlas et al IWC
0.088Z0.58
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Errors in Radar/Aircraft Observations

• Radar scans had to be slightly interpolated to
  match up with aircraft position (radar scans had
  to be virtually advected), introducing some
  error in the results
• Other errors arose from the aircraft sampling
  equipment and the in situ IWC equation used, and
  possibly the Cimarron radar itself

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Conclusions

• Existing Z-IWC schemes have significant errors
  because radar reflectivity from ice particles is
  a product of the IWC and the mass of the
  scatterers, and so two independent measurements
  are needed
• Polarimetric variables can provide the
  independent measurements. For this study, an
  equation was derived using Zh and the ratio of
  KDP to ZDR (shown to be practically insensitive
  to most shapes and densities of ice particles)
  which gave reasonable values of IWC
• This method works best for average-sized pristine
  crystals or moderately aggregated crystals. Once
  the aggregates grow to a spherical shape, ZDR
  lowers to near zero and the equation falters
  (overestimates the IWC)

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Questions?