Doppler Radar Basic Principles

Objectives Basic understanding of how to derive a wind field from Doppler radar measurements 2. Basic understanding of how a Doppler radar measures the radial velocity of “radar targets” 3. Understand how a radar’s Pulse Repetition Frequency (PRF) and wavelength l influence the maximum range/radial velocity that the radar can “resolve” (range folding; velocity aliasing  “Doppler Dilemma”) 4. Some exotica: a feel for a thing called “spectrum width”

Doppler Radar Basics Doppler radars measure three base moments: reflectivity, radial velocity and spectrum width Doppler radar sends short (~1 ms) pulses of wavelength l followed by a much longer listening period (~1 ms) In “pulse pair” processing: the radial velocity is derived from the phase shift between two successive pulses, NOT the phase shift of one individual pulse due to the target motion (this is an accuracy issue)

Determine a broadscale wind profile Some principles for “smooth” flows: Colour coding indicates whether radial velocities are inbound or outbound The “zero isodop” (ZI) separates regions of inbound and outbound radial velocities. Along the ZI the total wind is either tangential or zero. With increasing range radar samples flow at higher and higher altitudes.

outbound Wind Profile Backs With inbound Height. 1. Identify the ZI and regions of inbound/outbound velocity outbound inbound 2. Draw a straight line from the radar to a point on the ZI 3. Draw an arrow from inbound to outbound that is tangential to line 2 4. Repeat steps 2.+3. For other points on the ZI Wind Profile Backs With Height.

Velocity Azimuth Display (VAD) Can use a Doppler radar as a wind profiler if scatterers are present and horizontal wind shear is low (~uniform flow) Example: Uniform flow of 10 ms-1 from 360o vr R f -10 +10 -7 +7 90 180 135 360 45 270 225 315 -10 +10 +7 -7 f

Velocity Azimuth Display Estimate the wind velocity ~16 ms-1 wind from 205o

Range Folding - Example

Range Folding r t r/2 c t+T/4 r t+T/2 Radar sends 2 successive pulses at times t and t+T. Let r be the distance of a target from where pulse 1 can just return to the radar before pulse 2 is sent out: r t r/2 c t+T/4 r t+T/2

Range Folding r c r/2 t+3T/4 r r t+T Radar sends 2 successive pulses at times t and t+T. Let r be the distance of a target from where pulse 1 can just return to the radar before pulse 2 is sent out: r c r/2 t+3T/4 r r t+T During the time T the pulse travelled a distance 2r or cT, i.e. 2r = cT  rmax = cT/2

Velocity Aliasing - Example

Velocity Aliasing r r v t r+vT r+vT t+T vT Radar sends 2 successive pulses at times t and t+T. Let r be the distance of a target for pulse 1. The target travels with velocity v away from the radar, so that pulse 2 has to travel further: r r v t r+vT r+vT t+T vT Pulse 2 travels an extra distance 2vT. It is phase-shifted by 2vT compared to pulse 1.

Velocity Aliasing The phase-shifting of pulse 2 compared to pulse 1 can lead to ambiguities in the retrieved velocity: pulse at t pulse at t+T etc. Many different phase shifts can produce wave at t+T unless …

Velocity Aliasing … we restrict the permissable phase shifts in such a way that pulse 2 allows a non-ambiguous velocity interpretation: (remember: 2vT=extra distance travelled by pulse 2) We allow the wave to be shifted left/right by a maximum of half a wavelength l. It follows VN=|v| is the Nyquist velocity of the radar. If the target has a radial velocity w larger than the Nyquist velocity, w will be aliased back into the interval [-VN,+VN].

The Doppler Dilemma The maximum unambiguous range The maximum unambiguous velocity (Nyquist Velocity) The bigger Ru, the smaller VN The bigger VN, the smaller Ru

Doppler Dilemma – Escape Routes Buy an expensive S-band radar Run radar in “dual PRF” mode

Unfolding of a dual PRF signal aliased radial velocity vi +VN -2VN -VN +VN +2VN real radial velocity v -VN Velocity aliasing maps v into [-NV,+NV]. To “resolve” radial velocities beyond NV the dual PRF approach illuminates targets with 2 different PRFs with corresponding Nyquist velocities NV1, NV2. Measured radial velocities are v1 = v – n1*2VN1 (1) ni = (…,-2,-1,0,1,2,…) v2 = v – n2*2VN2 (2) (1),(2) express 2 relationships between 3 unknowns n1, n2, v. Running through the integers ni = (…,-2,-1,0,1,2,…) possible unfolded velocties v are …,vi-4NVi, vi-2VNi, vi, vi+2VNi, vi+4VNi,… C-band radar with Nyquist velocities NV1=13 ms-1 and NV2=9 ms-1 measures v1=-11 ms-1, v2=-3 ms-1 (1)  …,-63,-37,-11,+15,+41 ms-1 (2)  …,-39,-21,-3,+15,+33 ms-1 Match of smallest magnitude is +15 ms-1. Issues: (1) assume v the same in adjacent radials; (2) random v errors create artificial aliasing

Mesocyclone Example: Sydney 02 Feb 2005 Supercell

Spectrum Width

Spectrum Width R power radial velocity +10 +6 +1 3 2 1 -5 +1 +6 +10 Inside a pulse volume a distribution of various radial velocities (red arrows) exists. The standard deviation of this radial velocity distribution within the pulse volume is called spectrum width. The “radial velocity” for a pulse volume is an average of individual velocities derived from ~30 individual pulses. A measure of the true radial velocity distribution within the volume is the distribution of radial velocities from the 30 individual pulses. R +10 +6 +1 power real spectrum 3 2 measured spectrum 1 radial velocity -5 +1 +6 +10

Spectrum Width Velocity Width due mainly to Spectrum from small tornado Velocity Width due mainly to Turbulence within beam volume Wind shear (particularly vertical shear) across beam Beam geometry (radial component of a uniform wind field varies across beam)

Summary Basic understanding of how to derive a wind field from Doppler radar measurements 2. Basic understanding of how a Doppler radar measures the radial velocity of “radar targets” 3. Understand how a radar’s Pulse Repetition Frequency (PRF) and wavelength l influence the maximum range/radial velocity that the radar can “resolve” (range folding; velocity aliasing  “Doppler Dilemma”) 4. Some exotica: a feel for a thing called “spectrum width”