Estimation of some derived parameters from WP/RASS data sets

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• Estimation of some derived parameters from
  WP/RASS data sets
• BY
• Dr. (MRS) R.R. Joshi
• Indian Institute of Tropical Meteorology, Pune

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Project Title

• Establishment of wind profiler data archival and
  utilization Centre at IITM for Wind
  Profiler/Radio Acoustic Sounding System

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• The system is now being continuously operated
  since June 2003.
• Data Archival Status Hourly Averaged Vector Wind
  Data for the period June 2003 upto date.
• Data is archived on 40 GB DAT and CDS
• Data Format Text File (Height, u, v, w, ws
  wd)

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Quality Control checks of WP/RASS Data

• 1. Height continuity check on observed radial
  velocities has been incorporated with a multiple
  peak finding procedure for every range / height
  bin after an objective noise level estimation in
  the spectral domain using the Hildebrand and
  Sekhon(1) procedure as is standard in all wind
  profiler work including that at NOAA profilers in
  USA.

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• 2. The signal tracking procedure checks for
  continuity of the signal in adjacent range bins
  in the radial beam spectral data .The algorithm
  is similar, but not identical, to the adaptive
  tracking procedure used at NMRF Gadanki. The
  signal tracking window for tilted (east north)
  beams is typically set at of the unambiguous
  velocity for the radar measurement set. For the
  current operations this translates to a velocity
  window of 3m/sec . For the vertical wind the
  tracking window is set at 1 m/s.

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Consensus Averaging

• The consensus averaging procedure operates on the
  time series of radial velocity values (for tilted
  beams) obtained for a given range bin over the
  observation period (approx. 10 values in one
  hour). It assign weight to individual velocity
  values. Each velocity value is compared with
  itself and other values in the time series to
  check how many of these values fall within a
  velocity window of 5 mps. This number of
  velocity value falling within the window is
  called weight of that (observed) value. Weights
  are calculated for each velocity value. Only
  those observed values which have weights more
  than 4 out of 10 are used to calculate consensus
  average. For the vertical beam velocity window is
  set 1 mps.

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Computation of wind components

• From the consensusly averaged radial velocity
  values hourly average values of u and v are
  calculated by using formula
• U (Vre wsin
  ?) / cos ?
• V (Vrn - wsin
  ?) / cos ?
• Where ? is the elevation angle of the tilted
  beam.
• This procedure helps to eliminate outliers due to
  spiky noise or interference which is essential
  for quality control. The velocity window
  parameters as used above are typically same as
  used by NOAA researchers on the data of their 400
  MHZ profilers. After observing 6 minute and
  hourly data large shear in u and/orv is seen it
  seems only consensusly average is not adequate
  we need to introduce additional shear check
  condition on the consensusly passed u and v
  values.

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• If ui gt ui1 then lt 2 and
• If ui1 gt ui then lt 2
• If the condition is satisfied add the weight of
  ui as one with respect to ui1.
• Repeat this for all us (vs). Only those
  values of consensusly passed u (v) values which
  have a weight of greater 40 should be used for
  further calculations.

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Trend validation of WP/RASS data

• WP data is therefore compared for the trends
  with the available monthly average normal winds
  from RS/RW Santacruz, Mumbai, from 1955-1970,
  Pilot Balloon data of Pune from 1935-1970 and
  current monthly average of RS/RW data for
  Santacruz for the months June-September 2003.
  Above data are taken from IMD, Pune for both
  morning and evening ascents. This data is
  compared with WP/RASS data for four months . It
  is generally showing same trend for vector wind
  direction and vector wind speed.

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Wind Speed for July2003 (Evening)
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Wind Direction for July (evening)
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• Calculations of different atmospheric parameters
  from WP/RASS data
• In addition to measuring wind vector radar
  determines different atmospheric quantities from
  power, Doppler shift and Spectral width of
  returned signal. These are
• Strength of turbulence Cn2
• Eddy dissipation rate ? from sw2
• Momentum flux uw and vw

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• The structure constant for refractive index
  fluctuations Cn2
• Atmospheric turbulence is usually characterized
  by the refractive index structure constant Cn2 or
  eddy dissipation rate ? or sw2 Radars are
  sensitive to refractive index irregularities on
  scale half of the radar wave length.
  Backscattered power can therefore be used to
  infer the magnitude of refractive index structure
  constant
• If refractive index is n(ro) at ro position and
  refractive index is n(ror) at ror position then
  structure constant for refractivity turbulence in
  terms of the distance increment r is defined as
• 
  
  

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• (Green 1979, Gage 1990) defined Cn2 for locally
  homogeneous and isotropic inertial subrange
  turbulence as

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Cn2 derived from RS/RW

• Tatarskii (1971) shows that the turbulence
  structure constant for the radio refractivity
• Cn²
  
• Where a² 2.8
• ratio of eddy diffusivities
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• Lo Outer scale length of
  turbulence spectrum.
• M Vertical gradient of the
  refractive index.
• The Lo is presumed to be around 10 meters,
  although no direct evidence is available on the
  thickness of a turbulent layer Lo being of the
  order of the later. The value of the M is given
  by the following relation.

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Where p Atmospheric pressure in mbars.
T Absolute temperature. ?
potential temperature. q specific
humidity gm/kg. And hence the Cn²(radar) can be
given as Where F is the average fraction of
the radar volume which is turbulent and its value
is between .01and .1in lower troposphere.
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• Radar will detect turbulence only if the radar
  wave length lies in inertial subrange. If
  turbulence fills only a fraction F of radar
  sampled volume then Cn2 measured from radar will
  be less than value computed from radiosonde and
  one may therefore write as
• The value of F is ranging from 0.1 to 0.01 for
  troposphere

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Equivalent Reflectivity

• The wavelength dependencies are combined in the
  following equation which gives the amount of
  Rayleigh scattering expressed as radar
  reflectivity factor Z, that would produce the
  same amount of backscattered power as a given
  amount of clear air refractive index variability,
  which is denoted by the structure parameter Cn²
  
• At the wavelengths typically used by radar wind
  profilers, Rayleigh scattering from precipitation
  can equal or exceed the Bragg scattering.

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• Higher Cn2 values are observed in the active
  phase for the month of July 2003 . Same trend is
  observed in the RS/RW observations taken at
  Chikhalthana (19.85 0 N, 75.400 E) which is 230
  kms away from Pune.
• Ottersten, 1969 gave the volume reflectivity from
  clear air turbulent scattering in terms of Cn2.

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Radar Refractive index structure constant

• The mathematical expression for radar radio
  refractive index structure constant is given as
• 
  
• 
  
• Reflectivity is calculated from SNR that we
  get from wind profiler observations.
• Hence we can study the seasonal variation of
  refractive index structure constant using UHF
  radar.

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• The noise is estimated by Hildebrand algorithm
  and then S/N ratio is calculated.
• Substituting value of in above equation we can
  calculate value of Cn2
• Van Zandt proposed a method for the estimation of
  Cn2 by above equation and radar SNR values as

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• Where
• Pt transmitted power
• Ap Physical area of the antenna
• M No. of FFT pints
• P - No. of bins occupied by signal

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• Monthly averaged values of Cn2 have been
  calculated for three seasons i.e April, July,
  November 2003 as premonsoon, monsson and
  postmonsson season respectively. The values of
  log Cn2 vary from -17 to -14 order of magnitude.
• Below 2 - 3 kms level of humidity is higher
  therefore we observe high values of Cn2 which
  then decreases with height and hence Cn2
  correspondingly decreases.

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Diurnal variation of Cn2
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• On 12 June 2003 we obser diurnal variation in the
  Cn2 of the order of 10dB. From 1 km values are
  increases and have peak values around 1.85 kms
  which indicates the presence of the top of the
  boundary layer and then it starts decreasing.

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Kinetic energy dissipation rate ?

• Turbulent kinetic energy dissipation rate is one
  of the key parameter in the atmosphere turbulence
  theory. It represents rate of transfer of energy
  to smaller eddies in the inertial subrange of
  inhomogeneties and rate of conversion of kinetic
  energy of turbulence in to heat in the viscus
  subrange. Above boundary layer dissipation rate
  decreases rapidly to near zero and rising again
  in the vicinity of the jet stream. The
  estimation of epsilon is based on equations that
  follow from kolmogorov-obukhov laws of
  transformation of turbulent energy.

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• There are three methods proposed for the
  estimation of epsilon from the radar
  measurements. All these methods assume the
  turbulence is isotropic and in the inertial
  subrange. It is also assumed that the spectrum
  follows a Kolmogorov shape and the atmosphere is
  stably stratified. There are three methods of
  deriving the turbulence kinetic energy
  dissipation rate e from radar observation
• Doppler spectral width method
• Radar backscatter signal power method
• Wind variance method.
• The various assumptions and approximations
  involved in these methods.

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• In the first method for isotropic turbulence the
  velocity half-variance is given by
• Where kinetic energy density is given by
• E(k) a e2/3 k -5/3
• a - 1.6 Kolmogorov constant
• k wave number
• Thus e is directly related to the total velocity
  half variance.
• Frisch and Clifford integrated above equation
  assuming Gaussian beam width and pulse shape

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• s vw2 - Variance in vertical beam w within the
  pulse volume v

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• where

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• And

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• a - half the diameter of the circular beam cross
  section
• b - half length of the pulse
• ?2 - confluent hypergeometric expansion
  introduced by Labbitt for Frisch integral
• td-Dwell time for vertical beam Nc x IPP x P x
  I
• width described by above is the width of spectrum
  from 76 pulse series returning from a turbulent
  pulse volume.
• Gossard et al 1990 gave the equation as

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• Energy dissipation rate

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• The profile of eddy dissipation rate is also
  estimated from the vertical beam spectral width
  after applying due correction for the finite beam
  width of the profiler antenna Gossard (1998).

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• If the profiler is operating when it is
  raining /or hydrometers are present in the volume
  of atmosphere sensed by it, it measures
  essentially the fall velocity of the hydrometeors
  in the zenith beam position. The presence of
  hydrometeors/raindrops is clearly indicated by
  the zenith beam radial velocity which rises to
  values of more than 1 m/sec (Ralph) as against
  the clear air vertical velocities which are much
  lower than 1 m/sec. Under these conditions, the
  observed variance needs to be further corrected
  for the different fall speeds/spread in fall
  velocities of raindrops/hydrometeors.

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• sw2 sobs2 sa2 sD2
• sa2 - contribution to observed variance because
  of the finite beam width of the profiler antenna
• WS - hourly averaged wind velocity
• sD2 - variance contribution because of the
  different fall speeds of rain drops (Atlas et
  al). 1 m2 sec-2 as prescribed by Gossard
  Strauch

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Average energy dissipation rate for 25th July
2003
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• Second method
• Radar system constant poses some uncertainty
  unless a calibrated radar is used.
• Third method
• The vertical wind data is taken for one-two
  hours subjected to Fourier transform analysis and
  the resulting amplitude frequency spectrum is
  converted to power frequency spectrum. Wild data
  points are removed before analysis. The power
  spectrum at each height is examined to identify
  the Brunt Vaisala (BV) frequency N for that
  height. Weinstock showed inertial subrange
  extends upto the buoyancy scale (BV frequency).

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• The variance of the vertical wind due to
  turbulence is obtained by integrating the power
  spectrum of the vertical wind from BV frequency
  to Nyquist frequency.
• Hence ? is obtained by

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Some results by using WP/RASS data

• Findlater (1969) showed that the LLJs observed
  in peninsular/western India in July are a part of
  a branch of the Somali Jet (the high speed wind
  flow from Kenya to eastern Ethiopia Somalia)
  is well correlated with rainfall in western
  India. Since deep convection activity produces a
  significant amount of middle/upper level
  cloudiness, the relationship between LLJs and
  convective activity indicates that LLJs are
  important contributors to regional climate.

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• The appearance of LLJs with its core around 850
  to 500 hPa during the Asian summer monsoon
  (June-September) in the peninsular and western
  region of India is closely associated with the
  active/break periods in the monsoon (P.V. Joseph
  et al) In Defination of LLJ, Fay (1958) is
• The wind speed maximum exists below 6 km.
• The wind direction is substantially unaltered
  throughout the height range approximately
  within 40o around a mean persistent
  direction.
• The wind speed should sharply decrease on either
  side of the wind maximum.

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• We have therefore analyzed the wind profiler
  data with respect to LLJ particularly during an
  active phase of monsoon from 24 July to 28July
  2003 with emphasis on estimation of horizontal
  wind and associated shear, fluxes, energy
  dissipation rates and their diurnal variations.

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• The profile of eddy dissipation rate is also
  estimated from the vertical beam spectral width
  after applying all corrections. They have the
  peak near LLJ height.
• For the clear air case (precipitation cases
  excluded) the epsilon values near the lowest wind
  maximum are in the range of 2 10-4 to 4 10-4 m2
  sec-3as shown in figure . These ? values are
  comparable to those reported in the literature by
  Gossard et al. (1998), Satheesan et al. (2002),
  and Narayan Rao et al. (2001). When observations
  corresponding to the hydrometeors/rains are
  included such as on 24th, 25th and 27th July, the
  epsilon values near the lowest wind maximum are
  of the order of 10-3 increasing to 8.5 10-3 m2
  sec-3 on 27th July when heavy rains were
  observed, thus indicating high turbulence
  activity during rains .

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• The fluxes uw and vw are then calculated by
  calculating
• 
  (where bar represents average value)
• The profiles of average momentum flux and
  observed vertical velocities (excluding the
  precipitation cases) for the period 24th to 28th
  July is plotted in figure (10). The presence of
  upward air motions (positive vertical velocities)
  is seen throughout the lower atmosphere on all
  these days with predominantly downward momentum
  flux. The flux values lie in the range -0.7 to
  0.3 m2 s-2 except on 27th July where it shows
  mean upward flux at middle level. The broad
  regions of ascending motions as seen from the fig
  (10) probably mean that the LLJs produce a
  favorable thermodynamic environment for deep
  convection (Beebe and Bates 1955).

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Atmospheric subsidence and the surface
temperature variability in the pre-monsoon month
over a semi arid north peninsular Indian station
A case study

• The variability in the maximum temperature in the
  month of March 2004 over a station representative
  of semi arid region of north peninsular India has
  been studied.
• The vertical velocity data measured by UHF Wind
  Profiler, installed at Pune (18.310 N, 73.580 E)
  has been utilized. The wind profiler has typical
  height coverage of 6-10 km with a resolution of
  300 meters.
• Hourly averaged vertical wind velocity profiles
  were obtained four times a day, on a three hourly
  basis from 0800 to 1700 IST (Indian Standard
  Time) in March 2004.
• The factors governing the variability of surface
  temperature are (1) radiation, (2) advection and
  (3) subsidence..

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• 'Heat wave' is one of the hazardous weather
  conditions in the premonsoon season (March-May)
  and early part (June and July) of monsoon season
  over Indian subcontinent.
• The favorable factors for heat wave conditions to
  occur over a particular region
• (1) large region of warm dry air prevailing in
  the surrounding of that region and appropriate
  flow pattern for transporting hot air into the
  region of the study
• (2) absence of moisture over a depth of
  atmospheric column and
• (3) large amplitude anticyclonic flow in the
  vertical levels above a place (Chaudhury et al.,
  2000).
• Thus the key factor in the process is the
  subsidence or in more general terms 'vertical
  velocity'.

The time series of daily maximum temperatures
over Pune in March 2004. The dark line shows
the climatological mean value. It is seen that on
every day of the month the daily maximum
temperature was above normal.
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Role of advection in the surface temperature
variability
Figure The latitude-time cross section of the
daily maximum temperature distribution in March
2004

• The tilting of temperature isolines indicates the
  high temperatures are developed first in the
  northern latitudes and gradually move towards the
  southern latitudes.
• The three episodes are clearly seen.
• In the first one i.e. on 4th March a region of
  high temperatures is developed at latitude 28.31
  N and after 5 days the high temperatures are
  observed at 18.53 N on 9th March.
• The second episode is from 16 to 20 March and the
  third episode is from 23 to 27 March.
• There was an advection of warm air from northern
  to southern latitudes. The effect of the
  advection is to make the temperature distribution
  uniformly high.

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Role of subsidence in the surface temperature
variability

• The weather at any place is the ultimate result
  of actions of all the scales planetary to meso
  scale. The anomaly at individual station is
  mainly controlled by the mesoscale circulations.
  The collection of such individual anomalies at
  number of stations forms the large-scale picture.
  Thus it becomes appropriate to consider mesoscale
  behavior to understand the anomalies on the daily
  scale. Here is the advantage of the wind profiler

• The study revealed the existence of two cell
  structure in the vertical in the pre-monsoon
  season
• The lower cell consists of upward motion
  extending up to 2 - 3 km and the upper cell
  consists of the subsidence motions confined
  between 3 to 6 km.
• In the morning hours, the upward motion in the
  lower levels extends to maximum height of about 3
  km. With the progress of the day, the subsidence
  penetrates to the lower levels reaching around 1
  km in the evening hours.

Vertical distribution of profiler mean velocity
at four observational hours in March 2004.
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• When compared with the reanalysis velocities, the
  profiler velocities are found higher by one
  order.
• Large variations (s.d. 20 cm/sec) are observed
  in the individual wind profiler velocity
  profiles.
• The difference in the order of velocities is due
  to the fact that reanalysis velocities, computed
  using pressurewind relationships, are
  representative of synoptic scale motions.
• The profiler velocities are representative of
  meso scale motions.

The variation of profiler (shown by triangles)
and reanalysis (shown by filled circles)
velocities on individual days at 6 GMT for the
period 1 to 19 March 2004.
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• The advection dominates in the initial period.
  When the horizontal temperature gradient
  vanishes, the effect of advection becomes small.
• The effect of the solar radiation on the
  variability of the temperature has been removed
  by removing daily normals from the daily maximum
  temperatures.
• The subsidence occurs in the form of alternating
  boxes overlaid on each other. The total depth of
  the column, even if it is not continuous, adds to
  the warming and stability of the atmosphere.
• Hence the association between total depths of the
  atmosphere over which the subsidence occurs
  (subsidence depth) and the temperature anomaly
  has been studied.
• The maximum temperature occurs in the afternoon
  hours. However the precursor to daily anomalies
  in the maximum temperature may be seen in the
  temperature anomalies of the previous hours.

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• Conclusions
• In the beginning of the month, the surface
  temperatures over the northern regions become
  high due to increased incoming solar radiations
  (compared to previous month i.e. February)
  assisted by extensive land mass and remoteness of
  the sea.
• This develops a shallow low pressure area at the
  surface over the heated region. The advection of
  warm dry air due to northerly winds increases the
  surface temperatures over the southern parts of
  India. Once the advection occurs the temperature
  gradient reduces and then there is prevalence of
  uniform high temperatures over the country.

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• The additional positive temperature anomalies are
  generated due to the atmospheric subsidence. The
  anomalies are found to be proportional to the
  total depth of the atmospheric column over which
  the subsidence occurs. The subsidence acts
  towards the increasing temperatures.
• The unique vertical velocity data set obtained
  through wind profiler system has revealed the
  important role of the subsidence in the surface
  temperature variability quite explicitly.
• The two cell structure and the order of the
  vertical velocity brought out in this study will
  find useful in the validation of the meso scale
  models over the Indian region and in turn will be
  useful in improving the short range temperature
  forecasts over the region.

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• Future plans
• Analysis of vertical velocity spectra BV
  frequency estimation-- Radar bright band
  characteristics
• Reflectivity - rain rate (Z-R) interrelation
  through determination of best fit drop size
  distribution of the observed velocity spectrum.

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• Thank You