1. WEATHER SIGNALS Chapter 4 (Focus is on weather signals or echoes from radar resolution volumes filled with countless discrete scatterers---rain, insects, perturbations in atmospheric refractive index, etc.) 10/24-11/11/2013METR 50041

2. Weather Signal Characteristics Large dynamic range (100 million!) Signals are semi coherent Numerous scatterers in the radar resolution volume The choice instrument for weather surveillance is the pulsed polarimetric Doppler weather radar. Extracting information (i.e., fields of echo H, V power, Doppler velocity, and correlation of H, V echoes) involves processing of echoes that randomly fluctuate. 10/24-11/11/2013METR 50042

3. 10/24-11/11/2013METR 5004 Echoes (I or Q) from Distributed Scatterers (Fig. 4.1) Weather signals (echoes) mT s 3  c (  s ) ≈  t (  t = transmitted pulse width)

4. Resolution Volumes 10/24-11/11/2013METR 5004 Range resolution 150 m 4 Lightning detector

5. Echo samples from 16 Resolution Volumes (Fig. 4.3) T s = 768 ms 5

6. Gate 12 Signal Spectrum (Fig. 8.34) 10/24-11/11/2013METR 5004 MT s = 128x0.768 ms = 98.3 ms 12 spectra are averaged 6

7. Repeat of Fig. 4.3 7  c (mT s ) ≈ 2-4 ms

8. Statistics of Weather Signals I and Q are uncorrelated zero mean random variables with Gaussian probability density function (pdf) P has an exponential pdf Amplitude |V| has a Rayleigh pdf β has a uniform pdf β Thanks to Dr. Sebastian Torres 8

9. Weather Echo Statistics (Fig. 4.4) 10/24-11/11/2013METR 50049

10. Weighting Functions for Scatterers and the Weather Radar Equation (4.12) 10/24-11/11/2013METR 500410

11. Drop Size Distributions ( Fig. 8.3b) 10/24-11/11/2013METR 5004 (1948) (1943) (From drop sizes between 1 and 3 mm) 11

12. The Angular Weighting Function 10/24-11/11/2013METR 500412

13. The Measured Range Weighting Function for two Receiver Bandwidths (Fig. 4.6) 10/24-11/11/2013METR 500413

14. Range Weighting Function for Echoes Samples at Range Time τ s (Fig.4.7) 10/24-11/11/2013METR 5004 250 m 14

15. The Resolution Volume V 6 Fig. 5.11 Angular weighting function Range weighting function 10/24-11/11/2013METR 500415

16. Spectrum of a transmitted rectangular pulse 10/24-11/11/2013METR 5004 If receiver frequency response is matched to the spectrum of the transmitted pulse (an ideal matched filter receiver), some echo power will be lost. This is called the finite bandwidth receiver loss L r. For and ideal matched filter L r = 1.8 dB. 16 f t f

17. Receiver Loss Factor (Fig. 4.8) for a Gaussian receiver response and rectangular pulse (in general a matched condition is when B 6  =1) Eq.(4.28) 10/24-11/11/2013METR 5004 B 6 = 6 dB bandwidth of the receiver’s frequency response.  = transmitted pulse width 17 L r = 1.8 dB for an ideal matched receiver

18. Reflectivity Factor Z (Spherical scatterers; Rayleigh condition: D ≤ λ/16) 10/24-11/11/2013METR 500418

19. Reflectivity Factor of Spheroids (Horizontally Polarized Waves) p[D e,e,ξ ] = probability density σ h [D e, e, ξ ] = backscatter cross section for H pol. D e = equivalent volume diameter e = eccentricity of the spheroid scatterer ξ = angle between the symmetry axis and the electric field direction N 0 = the number density per unit diameter (m -4 ) 10/24-11/11/2013METR 500419

20. Differential Reflectivity in dB units: Z DR (dB) = Z h (dBZ) - Z v (dBZ) in linear units: Z dr = Z h (mm 6 m -3 )/Z v (mm 6 m -3 ) - is independent of drop concentration N 0 - depends on the shape of scatterers 10/24-11/11/2013METR 500420

21. 10/24-11/11/2013METR 500421 Shapes of raindrops falling in still air and experiencing drag force deformation. D e is the equivalent diameter of a spherical drop. Z DR (dB) is the differential reflectivity in decibels (Rayleigh condition is assumed). Adapted from Pruppacher and Beard (1970)

22. The Weather Radar Equation 10/24-11/11/2013METR 500422

23. Acquisition, Processing and Display of Weather radar data 1 2 M Range-time  s Time series of M power samples Base Data: P h, P v,v, SW, etc. Azimuthal Scan (constant elevation) Volume Coverage Pattern Product displays (e.g., CAPPI, etc.) Sample-time ss Data radial Radial of reflectivity factor Z (M power samples are processed to produce one Z estimate at r) Range r = c  s /2 (I 2 + Q 2 )

24. WSR-88D Thresholding Data Fields based on Signal to Noise Ratios Locations with non-significant powers are censored: -Non significant returns have a SNR below a user-defined threshold -The system allows a different threshold for each spectral moment 10/24-11/11/2013METR 500424

25. SNR> -3dB Z (dBZ)

26. SNR> 2dB Z (dBZ) 26

27. SNR> -0.5 dB

28. SNR> 3.5 dB

29. Weather Echo Power vs Range (WSR-88D) 10/24-11/11/2013METR 5004 P r =P n ≈6x10 -15 Watts 29