Precipitation studies with RADARS

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• Precipitation studies with RADARS
• and
• use of WP/RASS
• By
• S.H. Damle

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• In precipitating conditions a vertically pointing
  Doppler Radar Effectively measures the apparent
  fall velocity of the falling hydrometers/snow
  particles
• The scattering in most cases is presumed to be
  Rayleigh
• The apparent/observed fall velocity deviates from
  true fall velocity because of
• Ambient clear air velocity turbulence
• Pressure dependence of fall velocity
• Deviations from the assumed Rayleigh scattering
  mechanism

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• The ambient clear air velocity turbulence are
  the most important and must be known with
  reasonable accuracy/ confidence level to obtain
  the true fall velocities other related
  parameters from the observed apparent velocity
• The classical work of Atlas and Srivastav (1973)
  shows that the clear air updrafts/downdrafts
  should preferably be measured with accuracies of
  0.25 m/sec or better to obtain reasonable
  estimates of the rain related parameters

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• The conventional S/C/X band Radars can not quite
  measure the turbulent clear air motion the
  scale sizes of turbulence to which they could
  respond being much smaller ? /2
• In the absence of clear air velocity turbulence
  , Roger used an empirical relation like to
  utilise radar precipitation data
• ltVfgt 2.65 Z 0.107 m/sec
• since ltVobs gt Vf - w where w is positive for
  upward air motion.
• The Rogers empirical relationship is
  approximate within 1 m/sec

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• The advent of U/VHF Radars has now made possible
  direct measurement of ambient clear air
  updraft/downdraft and the turbulence.
• Simultaneous measurement of clear air turbulent
  air velocities and the hydrometeor (apparent)
  fall velocities make possible the precipitation
  studies with these Radars.

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The use of clear air wind profiler Radars

• Typical clear air Radar operating frequencies 50,
  400, 1380 MHz.
• Clear air scattering mechanism Bragg scatter
• - ?-1/3 dependence
• Precipitation - Rayleigh scatter - ?-4
  dependence
• If one equates the expressions for the volume
  reflectivity for the two cases one obtains the
  relationship between the equivalent reflectivity
  factor Ze the Cn2 Thus
• dBZe 10 log Ze 10 log 10 Cn2 log ?11/3
  15.31 where ? is in meters and Ze is in mm6/m3
• Equation is valid for scattering from water
  droplets
• Typical clear air Cn2 values are in the range of
  10-15 to 10-18 m-2/3

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Illustrative Table of Cn2 Ze
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• From this table one can note
• 50 MHz system would almost always measures the
  clear air velocity unless the precipitation rises
  beyond rain rate of few mm/hr
• 1380 MHz profiler is sensitive to smallest of
  drizzle (rain rate 0.01mm/hr) and swamps the
  clear air signal.
• This prompted research workers to use co-located
  or near by radars- one at 50 MHz and the other
  915/1380 MHz for precipitation study.
• The 400 MHz system case is intermediate between
  these two extremes and thus the 400 MHz profiler
  may be amenable to simultaneous observations of
  Bragg Rayleigh scatter.

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• Relationships to dropsize distribution
• Z ? D6 N (D) dD
• The first task is to relate fall velocity with
  drop diameter
• Vf aDb - unrealistic
• GK data shows that fall speed approaches an
  asymptotic value of 9.2 m/sec for D gt 6 mm
• Atlas , Srivastava modification
• V965-1030 exp (-6D) cm /sec, where D is in cm

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• Modified GK expression is valid near the ground
• For higher heights Foote Dutoit suggested a
  density correction factor to use them at higher
  heights
• Vh vg (?g/?h)0.4
• Thus if true fall velocity is calculated from
  radar observation, sample D values, within the
  limitation of spectral resolution, can be
  obtained for a given precipitation event.

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Key factors to prepare algorithm development

• Location in the Doppler plane of the Bragg
  Rayleigh scatter signal
• Ralphs prescriptions of velocity thresholds for
  Rayleigh scatter identification for rain
• The Rayleigh scatter signal for height levels
  just below and above the zero degree isotherm
  level

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• The bright band signature
• - Large velocities just below freezing level
  heights and steep fall in the speed towards
  freezing level heights indicative of presence
  of snow at/above freezing level
• - Absence of Bright Band indicative of
  presence of super cooled water droplets above
  freezing levels
• The (Doppler) velocity value in the case of
  snow/ice particulates is less than that of water
  droplets because of lower density of ice/snow
  compared to that of water

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Signal flow in a profiler

• Objective Determination of noise power
• Hildebrand/Sekhon algorithm
• Obtain average noise power/bin Pn
• standard deviation sn
• For a given range bin
• Subtract average noise power from spectral value
• Identify clear air spectral peak
• Identify precipitation spectra peak
• Fit Gaussian curve for clear air spectra and
  estimate clear air velocity and spread
• Deconvolve the ppt spectrum by clear air spectrum
  and obtain ppt spectral width

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• For lower rain rates it may be acceptable to fit
  Gaussian curve to ppt spectra and estimate
  apparent fall velocity and apparent spectral /
  observed width
• stp2 spo2- scl2
• True fall velocity observed velocity clear
  air velocity
• Calculate dBZ from estimated S/N

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• Illustration with common size distribution
• N(D) N0 exp (-?D)
• V 965 -1030 (?/(?6)) 7 cm /sec
• With knowledge of ? and sample value of D as
  obtained earlier one may estimate N0 for every
  measurement height by relating to Z as indicated
  earlier
• Variation of N0 and ? with height may provide by
  extrapolation estimation of expected distribution
  of ground
• The knowledge of variation of the distribution
  with time could possibly correlated with cloud
  models to study the evolution.

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Concluding Remarks

• Difficulties arise when
• Separate Bragg and Rayleigh scatter peaks can not
  be identified in the spectrum
• The topic is of current research interest
  April 2005 JOAT
• Use of iterative deconvolution.
• Works with additional external constraints in
  the algorithm since iterative methods can lead to
  divergent solutions
• Model spectra fitting is carried out using gamma
  distribution 400 MHz
• More work needed for the case when two distinct
  peaks can not be identified.