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

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

2. Project Title “Establishment of wind profiler data archival and utilization Centre at IITM for Wind Profiler/Radio Acoustic Sounding System”

3. 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)

4. 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.

5. 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.

6. 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.

7. 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 θ) / cos θ V = (Vrn - wsin θ) / cos θ Where θ 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.

8. If ui > ui+1 then < 2 and If ui+1 > ui then < 2 • If the condition is satisfied add the weight of ui as one with respect to ui+1. • Repeat this for all u’s (v’s). Only those values of consensusly passed u (v) values which have a weight of greater 40% should be used for further calculations.

9. 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.

10. Wind Speed for July2003 (Evening)

11. Wind Direction for July (evening)

12. 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 Є from σw2 • Momentum flux u’w’ and v’w’

13. The structure constant for refractive index fluctuations Cn2 • Atmospheric turbulence is usually characterized by the refractive index structure constant Cn2 or eddy dissipation rate Є or σw2 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(ro+r) at ro+r position then structure constant for refractivity turbulence in terms of the distance increment r is defined as

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

15. 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 ~ 1 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.

16. Where p = Atmospheric pressure in mbars. T = Absolute temperature. θ = 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.

17. 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

18. 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.

20. 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.

21. 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.

22. 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

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

25. 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.

26. Diurnal variation of Cn2

27. 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.

28. Kinetic energy dissipation rate Є • 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.

29. 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 ε from radar observation • Doppler spectral width method • Radar backscatter signal power method • Wind variance method. • The various assumptions and approximations involved in these methods.

30. In the first method for isotropic turbulence the velocity half-variance is given by Where kinetic energy density is given by E(k) = α ε2/3 k -5/3 α - 1.6 Kolmogorov constant k – wave number Thus ε is directly related to the total velocity half variance. Frisch and Clifford integrated above equation assuming Gaussian beam width and pulse shape

31. σ vw2 - Variance in vertical beam w within the pulse volume v

32. where

33. And

34. a - half the diameter of the circular beam cross section • b - half length of the pulse • γ2 - 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

35. Energy dissipation rate

36. 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).

37. 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.

38. σw2 = σobs2 – σa2 – σD2 • σa2 - contribution to observed variance because of the finite beam width of the profiler antenna • WS - hourly averaged wind velocity • σD2 - variance contribution because of the different fall speeds of rain drops (Atlas et al). = 1 m2 sec-2 as prescribed by Gossard & Strauch

39. Average energy dissipation rate for 25th July 2003

40. 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).

41. 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 Є is obtained by

42. Some results by using WP/RASS data Findlater (1969) showed that the LLJ’s 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 LLJ’s and convective activity indicates that LLJ’s are important contributors to regional climate.

43. The appearance of LLJ’s 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.

45. 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.

47. 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 Є 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 .

49. The fluxes u`w` and v`w` 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 LLJ’s produce a favorable thermodynamic environment for deep convection (Beebe and Bates 1955).